Find the value of the following expression:
20172 - 20162 + 20152 - 20142 + ... + 10032 - 10022
Given 5x+y−2z=37,3x−y+2z=11
Find the value of the following expression x+2y−4z.
We have \(\hept{\begin{cases}5x+y-2z=37\left(1\right)\\3x-y+2z=11\end{cases}}\)
\(\Leftrightarrow8x=48\)
\(\Leftrightarrow x=6\)
If x=6 then (1) will become \(y-2z=7\)
\(\Rightarrow2y-4z=14\)
\(\Rightarrow x+2y-2z=20\)
Find the minimum value of the expression .
Answer: The minimum value is
Bài này không khó cách làm thế này:
x2+y2+2x+2y+2xy+5 = (x2 + y2 +1 +2x + 2y+ 2xy)+4
= (x + y +1 )2 +4
Ta có ( x + y +1)2 >= 0 \(\Rightarrow\) ( x +y +1)2 +4 >= 4
Dấu "=" xảy ra khi và chỉ khi x=y=-0,5
Vậy Min(x+y+1)2 = 4 khi và chỉ khi x=y=-0,5.
Xong rồi đó. Có gì sai sót các bạn góp ý nhé.
x2 + y2 + 2x + 2y + 2xy + 5
= x2 + y2 + 12 + 2x + 2y + 2xy + 4
= (x + y + 1)2 + 4 \(\ge\) 4
Ta có : \(A=x^2+y^2+2x+2y+2xy+5=x^2+y^2+1^2+2xy+2.y.1+2.x.1+5-1\)
\(=\left(x+y+1\right)^2+4\ge4\)
Vậy Amin = 4
Find the minimum value of the expression \(\frac{2}{-4x^2+8x-5}\)
what is the value of following expression: 3X(3+7):2
Find the minimum value of the expression .
A=(x+y+1)(x+y+1)+4
A=(x+y+1)2+4
Vậy MinA=4 khi.......... của @Nguyễn Huy Thắng đó mà ghi tiếp
ngu Anh nhưng ko sao dịch dc chữ Find the minimum = tìm GTNN :)
\(A=x^2+y^2+2x+2y+2xy+5\)
\(=\left(x^2+y^2+2x+2y+2xy+1\right)+4\)
\(=\left(x+y+1\right)^2+4\ge4\)
Dấu "=" xảy ra khi \(\left(x+y+1\right)^2=0\)\(\Rightarrow x=-y-1\)
Vậy \(Min_A=4\) khi \(x=-y-1\)
Assume that two numbers x and y satisfy: 2x + y = 6.
Find the minimum value of expression A = 4x2 + y2
\(2x+y=6\)
\(\Rightarrow y=6-2x\)
\(\text{Thế vào phương trình ta dc:}\)
\(4x^2+\left(6-2x\right)^2\)
\(=4x^2+36-24x+4x^2\)
\(=8x^2-24x+36\)
\(\Leftrightarrow4x\left(2x-6\right)+36\)
Rồi sao nữa quên ùi
ta có : \(2x+y=6\Leftrightarrow y=6-2y\)
thay vào A, ta có:
\(A=4x^2+\left(6-2x\right)^2\)
\(A=8\left(x^2-3x+2,25\right)+18\)
\(A=8\left(x-1,5\right)^2+18\)
\(\Rightarrow A\ge18\)
what is the value of y in the following expression
(y+1)+(y+2)+(y+3)+(y+4)+(y+5)=50
(y + 1) + (y + 2) + (y + 3) + (y + 4) + (y + 5) = 50
y + 1 + y + 2 + y + 3 + y + 4 + y + 5 = 50
(y + y + y + y + y ) + (1 + 2 + 3 + 4 + 5) =50
y x (1 + 1 + 1 + 1 + 1) + 15 = 50
y x 5 + 15 = 50
y x 5 = 50 - 15
y x 5 = 35
y = 35 : 5
y = 7
Tính C = 1 2 – 2 2 + 3 2 – 4 2 + 5 2 – 6 2 + … . + 2013 2 – 2014 2 + 2015 2
C=12-22+32-42+52-62+..+20132-20142+20152
SSH:(20152-12):10+1=2015
(12-22)+(32-42)+(52-62)+...+(20132-20142)+20152
-10+(-10)+(-10)+...+(-10)+20152
-10x(2015-1):2+20152=12
=> C=12