\(2x^2+y^2+2x-2xy+5-4y=0\)

\(\Leftrightarrow\left[y^2-2y\left(x+2\right)+\left(x+2\right)^2\right]+\left(x^2-2x+1\right)=0\)

\(\Leftrightarrow\left(y-x-2\right)^2+\left(x-1\right)^2=0\)

\(\Leftrightarrow\left[{}\begin{matrix}y-x-2=0\\x-1=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=1\\y=3\end{matrix}\right.\)

\(S=\left(x+2\right)^2+\left(y-1\right)^2=\left(1+2\right)^2+\left(3-1\right)^2\)

\(=3^2+2^2=13\)

\(A=\left(2x-1\right)^2+9\ge9\\ A_{min}=9\Leftrightarrow x=\dfrac{1}{2}\\ B=2\left(x^2-2\cdot\dfrac{3}{4}x+\dfrac{9}{16}\right)+\dfrac{1}{8}=2\left(x-\dfrac{3}{4}\right)^2+\dfrac{1}{8}\ge\dfrac{1}{8}\\ B_{min}=\dfrac{1}{8}\Leftrightarrow x=\dfrac{3}{4}\\ C=\left(4x^2+4xy+y^2\right)+2\left(2x+y\right)+1+\left(y^2+4y+4\right)-4\\ C=\left[\left(2x+y\right)^2+2\left(2x+y\right)+1\right]+\left(y+2\right)^2-4\\ C=\left(2x+y+1\right)^2+\left(y+2\right)^2-4\ge-4\\ C_{min}=-4\Leftrightarrow\left\{{}\begin{matrix}2x=-1-y\\y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{3}{2}\\y=-2\end{matrix}\right.\)

\(D=\left(3x-1-2x\right)^2=\left(x-1\right)^2\ge0\\ D_{min}=0\Leftrightarrow x=1\\ G=\left(9x^2+6xy+y^2\right)+\left(y^2+4y+4\right)+1\\ G=\left(3x+y\right)^2+\left(y+2\right)^2+1\ge1\\ G_{min}=1\Leftrightarrow\left\{{}\begin{matrix}3x=-y\\y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2}{3}\\y=-2\end{matrix}\right.\)

\(H=\left(x^2-2xy+y^2\right)+\left(x^2+2x+1\right)+\left(2y^2+4y+2\right)+2\\ H=\left(x-y\right)^2+\left(x+1\right)^2+2\left(y+1\right)^2+2\ge2\\ H_{min}=2\Leftrightarrow\left\{{}\begin{matrix}x=y\\x=-1\\y=-1\end{matrix}\right.\Leftrightarrow x=y=-1\)

Ta luôn có \(\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2\ge0\)

\(\Leftrightarrow2x^2+2y^2+2z^2-2xy-2yz-2xz\ge0\\ \Leftrightarrow x^2+y^2+z^2\ge xy+yz+xz\\ \Leftrightarrow x^2+y^2+z^2+2xy+2yz+2xz\ge3xy+3yz+3xz\\ \Leftrightarrow\left(x+y+z\right)^2\ge3\left(xy+yz+xz\right)\\ \Leftrightarrow\dfrac{3^2}{3}\ge xy+yz+xz\\ \Leftrightarrow K\le3\\ K_{max}=3\Leftrightarrow x=y=z=1\)

\(a)2xy+4y-x=5\)

\(\Leftrightarrow\left(2xy+4y\right)-x=3+2\)

\(\Leftrightarrow2y\left(x+2\right)-x-2=3\)

\(\Leftrightarrow2y\left(x+2\right)-\left(x+2\right)=3\)

\(\Leftrightarrow\left(x+2\right)\left(2y-1\right)=3\)

\(\Rightarrow\left(x+2\right);\left(2y-1\right)\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)

Xét từng trường hợp :

Vậy

\(2x+y=xy-3\)

\(\Leftrightarrow xy-2x-y=3\)

\(\Leftrightarrow\left(xy-2x\right)-y=-2+5\)

\(\Leftrightarrow x\left(y-2\right)-y+2=5\)

\(\Leftrightarrow x\left(y-2\right)-\left(y-2\right)=5\)

\(\Leftrightarrow\left(y-2\right)\left(x-1\right)=5\)

\(\Rightarrow\left(y-2\right);\left(x-1\right)\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

Xét các trường hợp như câu trên và kết luận

\(2xy+4y-x=5\)

\(\Rightarrow2y\left(x+2\right)-\left(x+2\right)=5-2\)

\(\Rightarrow\left(x+2\right)\left(2y-1\right)=3\)

\(\Rightarrow\left(x+2\right);\left(2y-1\right)\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)

Ta xét bảng 

Vậy.......................................................

\(2x+y=xy-3\)

\(\Rightarrow2x+y-xy=3\)

\(2x-2+y\left(x-1\right)=3-2\)

\(\Rightarrow2\left(x-1\right)+y\left(x-1\right)=1\)

\(\Rightarrow\left(2+y\right)\left(x-1\right)=1\)

\(\Rightarrow\left(x-1\right);\left(2+y\right)\inƯ\left(1\right)=\left\{\pm1\right\}\)

Xét bảng 

Vậy..........................

Lời giải:

a. $x^2+y^2+4y+13-6x$

$=(x^2-6x+9)+(y^2+4y+4)$

$=(x-3)^2+(y+2)^2$

b.

$4x^2-4xy+1+2y^2-2y$

$=(4x^2-4xy+y^2)+(y^2-2y+1)$

$=(2x-y)^2+(y-1)^2$

c.

$x^2-2xy+2y^2+2y+1$

$=(x^2-2xy+y^2)+(y^2+2y+1)$

$=(x-y)^2+(y+1)^2$

a. \(x^2+y^2+4y+12-6x=\left(x^2-6x+9\right)+\left(y^2+4y+4\right)=\left(x-3\right)^2+\left(y+2\right)^2\)b. \(4x^2-4xy+1+2y^2-2y=\left(4x^2-4xy+y^2\right)+\left(y^2-2y+1\right)=\left(2x-y\right)^2+\left(y-1\right)^2\)c. \(x^2-2xy+2y^2+2y+1=\left(x^2-2xy+y^2\right)+\left(y^2+2y+1\right)=\left(x-y\right)^2+\left(y+1\right)^2\)

a: \(x^2-6x+y^2+4y+13\)

\(=x^2-6x+9+y^2+4y+4\)

\(=\left(x-3\right)^2+\left(y+2\right)^2\)

b: \(4x^2-4xy+1+2y^2-2y\)

\(=4x^2-4xy+y^2+y^2-2y+1\)

\(=\left(2x-y\right)^2+\left(y-1\right)^2\)

c: \(x^2-2xy+2y^2+2y+1\)

\(=x^2-2xy+y^2+y^2+2y+1\)

\(=\left(x-y\right)^2+\left(y+1\right)^2\)

The Kinh are also known as the Vietnamese, and Son La is the second largest group, accounting for 18% of the province's population. Population is concentrated in urban areas. Kinh language in Vietnamese - Muong language. Apart from the part of ethnic minorities residing in Son La area, many people have just moved from the North and North Central Plains. Especially since listening to the call of the Party to build mountainous economic development, Kinh people from the delta provinces to Son La; The family of Dien Bien Phu campaign soldiers stayed in the mountainous region. At present, some areas in the province of Kinh ethnic minorities include Kinh people in Hai Duong, Hung Yen and Thai Binh provinces in Song Ma and Yen Chau districts; Thai Binh province in Thuan Chau, Ha Tay province in Mai Son and so on.Kinh people living in Son La are interspersed with ethnic minority people. They quickly integrate in production, cultural exchange and solidarity to create cohesion and development in Son land. Leaves. The Kinh are also called Vietnamese. The Kinh language belongs to the Viet-Muong language group. Kinh people do farming. In the wet rice cultivation, the Kinh people have traditionally built dikes, ditches. Horulture, mulberry growing, livestock and poultry husbandry, river fishing and marine fish development. Pottery is very early. Kinh people have habits betel betel, drinking tea, water. In addition to fried rice, sky rice, also porridge, sky rice. Shrimp sauce, duck eggs flipped is a unique dish of the Kinh.The Kinh village is often surrounded by bamboo, and there is a strong village gate in many places. Each village has a communal meeting place and worship. Kinh people live in the land. In the Kinh family, the husband (the father) is the owner. Children take their father and father's relatives as "family", while mother is "grandfather". The first son was responsible for organizing the worship of his parents, grandparents. Each of them has their own church, with their heads in charge of their work. Monogamy marriage The wedding is going through many rituals, the boy asked his wife and married his wife. After the wedding, the bride returns home. The men respect virginity, virtue of the bride, and pay attention to their background.The ancestor worshipers of the Kinh. The deceased are sacrificed by their descendants every year on the day they die. Their graves are regularly visited by relatives and carers. Every year the farmer has a series of festivals and festivals associated with farmer beliefs. In addition, Buddhism, Taoism, Taoism, Catholicism from the outside came into being received at different levels. The literary capital of the Kinh is quite large: oral literature (stories, folk songs, proverbs), literary literature (poetry, literature, books). Early and advanced art in many respects: singing, music, sculpture, painting, dancing, singing. The annual village festival is one of the most exciting and lively events in the countryside.

The Kinh are also known as the Vietnamese, and Son La is the second largest group, accounting for 18% of the province's population. Population is concentrated in urban areas. Kinh language in Vietnamese - Muong language. Apart from the part of ethnic minorities residing in Son La area, many people have just moved from the North and North Central Plains. Especially since listening to the call of the Party to build mountainous economic development, Kinh people from the delta provinces to Son La; The family of Dien Bien Phu campaign soldiers stayed in the mountainous region. At present, some areas in the province of Kinh ethnic minorities include Kinh people in Hai Duong, Hung Yen and Thai Binh provinces in Song Ma and Yen Chau districts; Thai Binh province in Thuan Chau, Ha Tay province in Mai Son and so on.Kinh people living in Son La are interspersed with ethnic minority people. They quickly integrate in production, cultural exchange and solidarity to create cohesion and development in Son land. Leaves. The Kinh are also called Vietnamese. The Kinh language belongs to the Viet-Muong language group. Kinh people do farming. In the wet rice cultivation, the Kinh people have traditionally built dikes, ditches. Horulture, mulberry growing, livestock and poultry husbandry, river fishing and marine fish development. Pottery is very early. Kinh people have habits betel betel, drinking tea, water. In addition to fried rice, sky rice, also porridge, sky rice. Shrimp sauce, duck eggs flipped is a unique dish of the Kinh.The Kinh village is often surrounded by bamboo, and there is a strong village gate in many places. Each village has a communal meeting place and worship. Kinh people live in the land. In the Kinh family, the husband (the father) is the owner. Children take their father and father's relatives as "family", while mother is "grandfather". The first son was responsible for organizing the worship of his parents, grandparents. Each of them has their own church, with their heads in charge of their work. Monogamy marriage The wedding is going through many rituals, the boy asked his wife and married his wife. After the wedding, the bride returns home. The men respect virginity, virtue of the bride, and pay attention to their background.The ancestor worshipers of the Kinh. The deceased are sacrificed by their descendants every year on the day they die. Their graves are regularly visited by relatives and carers. Every year the farmer has a series of festivals and festivals associated with farmer beliefs. In addition, Buddhism, Taoism, Taoism, Catholicism from the outside came into being received at different levels. The literary capital of the Kinh is quite large: oral literature (stories, folk songs, proverbs), literary literature (poetry, literature, books). Early and advanced art in many respects: singing, music, sculpture, painting, dancing, singing. The annual village festival is one of the most exciting and lively events in the countryside.

The Kinh are also known as the Vietnamese, and Son La is the second largest group, accounting for 18% of the province's population. Population is concentrated in urban areas. Kinh language in Vietnamese - Muong language. Apart from the part of ethnic minorities residing in Son La area, many people have just moved from the North and North Central Plains. Especially since listening to the call of the Party to build mountainous economic development, Kinh people from the delta provinces to Son La; The family of Dien Bien Phu campaign soldiers stayed in the mountainous region. At present, some areas in the province of Kinh ethnic minorities include Kinh people in Hai Duong, Hung Yen and Thai Binh provinces in Song Ma and Yen Chau districts; Thai Binh province in Thuan Chau, Ha Tay province in Mai Son and so on.Kinh people living in Son La are interspersed with ethnic minority people. They quickly integrate in production, cultural exchange and solidarity to create cohesion and development in Son land. Leaves. The Kinh are also called Vietnamese. The Kinh language belongs to the Viet-Muong language group. Kinh people do farming. In the wet rice cultivation, the Kinh people have traditionally built dikes, ditches. Horulture, mulberry growing, livestock and poultry husbandry, river fishing and marine fish development. Pottery is very early. Kinh people have habits betel betel, drinking tea, water. In addition to fried rice, sky rice, also porridge, sky rice. Shrimp sauce, duck eggs flipped is a unique dish of the Kinh.The Kinh village is often surrounded by bamboo, and there is a strong village gate in many places. Each village has a communal meeting place and worship. Kinh people live in the land. In the Kinh family, the husband (the father) is the owner. Children take their father and father's relatives as "family", while mother is "grandfather". The first son was responsible for organizing the worship of his parents, grandparents. Each of them has their own church, with their heads in charge of their work. Monogamy marriage The wedding is going through many rituals, the boy asked his wife and married his wife. After the wedding, the bride returns home. The men respect virginity, virtue of the bride, and pay attention to their background.The ancestor worshipers of the Kinh. The deceased are sacrificed by their descendants every year on the day they die. Their graves are regularly visited by relatives and carers. Every year the farmer has a series of festivals and festivals associated with farmer beliefs. In addition, Buddhism, Taoism, Taoism, Catholicism from the outside came into being received at different levels. The literary capital of the Kinh is quite large: oral literature (stories, folk songs, proverbs), literary literature (poetry, literature, books). Early and advanced art in many respects: singing, music, sculpture, painting, dancing, singing. The annual village festival is one of the most exciting and lively events in the countryside.

x=2/3.dam bao dug lun.

9x³ - 6x² + 12x = 8

<=> 9x³ - 6x² + 12x - 8 = 0

<=> ( 9x³ - 6x² ) + ( 12x - 8 ) = 0

<=> 3x²( 3x - 2 ) + 4( 3x - 2 ) = 0

<=> ( 3x - 2 )( 3x² + 4 ) = 0

Vì 3x² + 4 ≥ 4 > 0 ∀ x

=> 3x - 2 = 0 <=> x = 2/3

Vậy ...

Trả lời:

9x³ - 6x² + 12x = 8

<=> 9x³ - 6x² + 12x - 8 = 0

<=> (9x³ - 6x²) + (12x - 8) = 0

<=> 3x²(3x - 2) + 4(3x - 2) = 0

<=> (3x - 2) (3x² + 4) = 0

<=> 3x - 2 = 0 hoặc 3x² + 4 = 0

<=> 3x = 2                 3x² = -4 (vô lí, vì 3x² \(\ge0\forall x\))

<=> x = \(\frac{2}{3}\)

Vậy \(S=\left\{\frac{2}{3}\right\}\)

\(2xy-2x-y=1\)\(\Leftrightarrow2x\left(y-1\right)-y=1\)

\(\Leftrightarrow2x\left(y-1\right)-y+1=1+1\)

\(\Leftrightarrow2x\left(y-1\right)-\left(y-1\right)=2\)

\(\Leftrightarrow\left(2x-1\right)\left(y-1\right)=2\)

Vì \(2x-1\)là số lẻ \(\Rightarrow2x-1\)thuộc ước lẻ của 2

Lập bảng giá trị ta có: 

Vậy các cặp giá trị \(\left(x;y\right)\)thoả mãn là: \(\left(0;-1\right)\), \(\left(1;3\right)\)

Bn ơi tại sao

2x.(y-1)-(y-1)=2

<=>(2x-1).(y-1)=2 được z?

Vì \(2x\left(y-1\right)-\left(y-1\right)=2x\left(y-1\right)-1\left(y-1\right)=\left(2x-1\right)\left(y-1\right)\)