Bai 1:
a, cho x+y=7 . Tinh M= (x+y)3+2x2+4xy+2y2
b, cho x-y=7 . Tinh A = x.(x+2)+y.(y-2)-2xy+37
GIUP MINH NHA, THANK YOU!^^
Bai 1:
Cho x-y=7. Tinh A= x.(x+2)+y.(y-2)-2xy+37
Giup minh vs nha, THANK YOU VERY MUCH !^^
\(A=x\left(x+2\right)+y\left(y-2\right)-2xy+37\)
\(=x^2+2x+y^2-2y-2xy+37\)
\(=\left(x^2-2xy+y^2\right)+2\left(x-y\right)+37\)
\(=\left(x-y\right)^2+2\left(x-y\right)+37\)
Thay x - y = 7
\(\Rightarrow A=49+14+37=100\)
Vậy A = 100 khi x - y = 7
a, Cho x - y = 7. Tinh
A = x( x + 2 ) + y( y - 2 ) - 2xy + 37
b, Cho x + 2y = 5. Tinh
B = x2 + 4y2 - 2x + 10 + 4xy - 4y
a, Ta có
A= x(x+2)+y(y-2)-2xy +37
=x2+2x+y2-2y-2xy+37
=x2-2xy+y2+2(x-y)+37
=(x-y)2+2(x-y)+37
Vì x-y=7
=>(x-y)2+2(x-y)+37=72+14+37=100
KL
b, Ta có B=x2+4y2-2x+10+4xy-4y
=x2+4xy+4y2-2x-4y+10
=(x+2y)2-2(x+2y)+10
Vì x+2y=5
=>(x+2y)2-2(x+2y)+10=52-10+10=25
KL
giup minh bai nay nha
cho x+y=7,xy=10 tinh gtbt
(x+Y)(x^2+y^2)(x^3+y^3)
a,cho \(x-y=7\), Tinh GT cua BT : \(A=x\left(x+2\right)+y\left(y-2\right)-2xy+37\)
b,cho x+2y =5, Tinh GT cua BT : \(B=x^2+4y^2-2x+10+4xy-4y\)
a) \(A=x\left(x+2\right)+y\left(y-2\right)-2xy+37\)
\(A=x^2+2x+y^2-2y-2xy+37\)
\(A=\left(x^2-2xy+y^2\right)+\left(2x-2y\right)+37\)
\(A=\left(x-y\right)^2+2\left(x-y\right)+37\)
Mà \(x-y=7\)
\(\Rightarrow A=7^2+2.7+37\)
\(A=100\)
b) \(B=x^2+4y^2-2x+10+4xy-4y\)
\(B=\left(x^2+4xy+4y^2\right)-\left(2x+4y\right)+10\)
\(B=\left(x+2y\right)^2-2\left(x+2y\right)+10\)
Mà \(x+2y=5\)
\(\Rightarrow B=5^2-2.5+10\)
\(B=25\)
Bai 1: Cho x+y= 5 , xy= 6. Khong tinh x,y hay tinh
a, \(\dfrac{1}{x}+\dfrac{1}{y}\)
b, x2 + y2
c, x-y
Giup minh vs bai nay kho qua, Thanks nhieu !^_^
b: \(x^2+y^2=\left(x+y\right)^2-2xy=25-12=13\)
c: \(\left(x-y\right)^2=\left(x+y\right)^2-4xy=5^2-4\cdot6=1\)
=>x-y=1 hoặc x-y=-1
bai 1:tim GTNN cua bieu thuc
A=x2+3x+7
B=(x-2)(x-5)(x2-7x-10)
bai 2:tim GTLN cua bieu thuc
A=11-10x-x2
B=[x-4](2-[x-4])
bai 3:tim x,y sao cho
A=2x2+9y2-6xy-6x-12y+2016 co GTNN
B=-x2+2xy-4y2+2x+10y-8 co GTLN
bai 4 :
a)cho x+y=3;x2+y2=5.tinh x3+y3
b)cho x-y=5;x2+y2=15.tinh x3-y3
Cho x+y=5 tính giá trị của biểu thức
A=x^3+y^3-2x^2-2y^2+3xy(x+y)-4xy+3(x+y)+10
Chox-y=7 Tính
B=x(x+2)+y(y-2)-2xy+37
Cho x+2y=5 Tính
C=x^2+4y^2-2x+10+4xy-4y
Câu 2:
\(B=x^2+2x+y^2-2x-2xy+37\)
\(=\left(x^2-2xy+y^2\right)+2\left(x-y\right)+37\)
\(=\left(x-y\right)^2+2\left(x-y\right)+37\)
\(=7^2+2\cdot7+37=49+37+14=100\)
Câu 3:
\(C=\left(x^2+4xy+4y^2\right)-2\left(x+2y\right)+10\)
\(=\left(x+2y\right)^2-2\left(x+2y\right)+10\)
\(=5^2-2\cdot5+10=25\)
BAI 1.phan tich cac da thuc sau thanh nhan tu:
a,2x^2-2xy-5x+5y
b,8x^2+4xy-2ax-ay
c,x^3-4x^2+4x
d,2xy-x^2-y^2+16
e,x^2-y^2-2yz-z^2
g,3a^2-6ab+3b^2-12c^2
BAI 2.tinh nhanh
a,37,5.8,5-7,5.3,4-6,6.7,5+1,5.37,5
b,35^2+40^2-25^2+80.35
BAI 3. Tim x biet:
a,x^3-1/9x=0
b,2x-2y-x^2+2xy-y^2=0
c,x(x-3)+x-3=0
d,x^2(x-3)+27-9x=0
BAI 4.Phan tich cac da thuc sau thanh nhan tu
a,x^2-4x+3
goi y :tach-4x=-x3xhoac tach3=-1+4
b,x^2+x-6
c,x^2-5x+6
d,x^4+4 (goi y:them va bot 4x^2)
BAI 5.Chung minh rang;
(3n+4)^2-16 chia het cho 3 voi moi so nguyen n.
BAI 6.Tinh gia tri cua bieu thuc sau:
M=a^3-a^2b-ab^2+b^3 voi a=5,75:b=4,25
BAI 7.Tim x biet:
a,x^2+x=6
b,6x^3+x^2=2x
Bài 1 câu g bạn kia làm sai mình sửa lại nhá
\(3a^2-6ab+3b^2-12c^2\)
\(=3\left(a^2-2ab+b^2\right)-12c^2\)
\(=3\left(a-b\right)^2-12c^2\)
\(=3\left[\left(a-b\right)^2-4c^2\right]\)
\(=3\left(a-b-2c\right)\left(a-b+2c\right)\)
Để mình làm tiếp cho :))
Bài 2 :
Câu a : \(37,5.8,5-7,5.3,4-6,6.7,5+1,5.37,5\)
\(=\left(37,5.8,5+1,5.37,5\right)-\left(7,5.3,4+6,6.7,5\right)\)
\(=37,5\left(8,5+1,5\right)-7,5\left(3,4+6,6\right)\)
\(=37,5.10-7,5.10\)
\(=10.30=300\)
Câu b : \(35^2+40^2-25^2+80.35\)
\(=\left(35^2+80.35+40^2\right)-25^2\)
\(=\left(30+45\right)^2-25^2\)
\(=75^2-25^2\)
\(=\left(75+25\right)\left(75-25\right)\)
\(=100.50=5000\)
Bài 3 :
Câu a : \(x^3-\dfrac{1}{9}x=0\)
\(\Leftrightarrow x\left(x^2-\dfrac{1}{9}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2-\dfrac{1}{9}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=\pm\dfrac{1}{3}\end{matrix}\right.\)
Câu b : \(2x-2y-x^2+2xy-y^2=0\)
\(\Leftrightarrow2\left(x-y\right)-\left(x-y\right)^2=0\)
\(\Leftrightarrow\left(x-y\right)\left(2-x+y\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-y=0\\2-x+y=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=y\\x+y=2\Rightarrow x=2-y\end{matrix}\right.\)
Câu c :
\(x\left(x-3\right)+x-3=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
\(x^2\left(x-3\right)+27-9x=0\)
\(\Leftrightarrow x^2\left(x-3\right)-9\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x^2-9\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x^2-9=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=\pm3\end{matrix}\right.\)
Bài 4 :
Câu a :
\(x^2-4x+3\)
\(=x^2-x-3x+3\)
\(=\left(x^2-x\right)-\left(3x-3\right)\)
\(=x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(x-1\right)\left(x-3\right)\)
Câu b :
\(x^2+x-6\)
\(=x^2-2x+3x-6\)
\(=x\left(x-2\right)+3\left(x-2\right)\)
\(=\left(x-2\right)\left(x+3\right)\)
Câu c :
\(x^2-5x+6\)
\(=x^2-2x-3x+6\)
\(=\left(x^2-2x\right)-\left(3x-6\right)\)
\(=x\left(x-2\right)-3\left(x-2\right)\)
\(=\left(x-2\right)\left(x-3\right)\)
Câu d :
\(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)
Bài 1:
a) \(2x^2-2xy-5x+5y\)
\(=\left(2x^2-2xy\right)-\left(5x-5y\right)\)
\(=2x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(2x-5\right)\)
b) \(8x^2+4xy-2ax-ay\)
\(=\left(8x^2+4xy\right)-\left(2ax+ay\right)\)
\(=4x\left(2x+y\right)-a\left(2x+y\right)\)
\(=\left(2x+y\right)\left(4x-a\right)\)
c) \(x^3-4x^2+4x\)
\(=x\left(x^2-4x+4\right)\)
\(=x\left(x-2\right)^2\)
d) \(2xy-x^2-y^2+16\)
\(=-\left[\left(x^2-2xy+y^2\right)-16\right]\)
\(=-\left[\left(x-y\right)^2-4^2\right]\)
\(=-\left[\left(x-y-4\right)\left(x-y+4\right)\right]\)
e) \(x^2-y^2-2yz-z^2\)
\(=-\left[\left(z^2+2yz+y^2\right)-x^2\right]\)
\(=-\left[\left(z+y\right)^2-x^2\right]\)
\(=-\left[\left(z+y+x\right)\left(z+y-x\right)\right]\)
g) \(3a^2-6ab+3b^2-12c^2\)
\(=\left(3a^2-6ab+3b^2\right)-12c^2\)
\(=\left(\sqrt{3a}+\sqrt{3b}\right)^2-12c^2\)
\(=\left(\sqrt{3a}+\sqrt{3b}+\sqrt{12c}\right)\left(\sqrt{3a}+\sqrt{3b}-\sqrt{12c}\right)\)
a) Cho x+y=7 tính: A= (x+y)^3 + 2x^2 + 4xy + 2y^2
B) cho x-y=-5 tính: B= (x-y)^3 - x^2 + 2xy - y^2
a) Ta có: A = (x + y)3 + 2x2 + 4xy + 2y2
A = 73 + 2(x2 + 2xy + y2)
A = 343 + 2(x + y)2
A = 343 + 2. 72
A = 343 + 98 = 441
b) B = (x - y)3 - x2 + 2xy - y2
=> B = (-5)3 - (x2 - 2xy + y2)
=> B = -125 - (x - y)2
=> B = -125 - (-5)2
=> B = -125 - 25 = -150