2^x+2^y=2^x+^y
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20 tháng 12 2021
\(a,=\dfrac{x^2-2xy+y^2}{\left(x-y\right)\left(x+y\right)}=\dfrac{\left(x-y\right)^2}{\left(x-y\right)\left(x+y\right)}=\dfrac{x-y}{x+y}\\ b,=\dfrac{x^2+2xy+y^2-x^2+2xy-y^2-4y^2}{\left(x-y\right)\left(x+y\right)}=\dfrac{4xy-4y^2}{\left(x-y\right)\left(x+y\right)}=\dfrac{4y\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}=\dfrac{4y}{x+y}\)
31 tháng 7 2016
a) \(\left(x+y\right)^2+\left(x-y\right)^2+\left(x+y\right)\left(x-y\right)\)
\(=x^2+2xy+y^2+x^2-2xy+y^2+x^2-y^2\)
\(=3x^2+y^2\)
b)\(\left(3x+y\right)^2+\left(3x-y\right)^2-\left(2x+y\right)\left(2x-y\right)\)
\(=9x^2+6xy+y^2+9x^2-6xy+y^2-4x^2+y^2\)
\(=14x^2+3y^2\)
c) \(2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2+\left(x-y\right)^2\)
\(=\left(x-y\right)^2+2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2\)
\(=\left(x-y+x+y\right)^2\)
\(=4x^2\)
d)\(-2\left(x^2-9y^2\right)+\left(x-3y\right)^2+\left(x+3y\right)^2\)
\(=\left(x+3y\right)^2-2\left(x+3y\right)\left(x-3y\right)+\left(x-3y\right)^2\)
\(=\left(x+3y-x+3y\right)^2=9y^2\)
KK
1
DT
Dang Tung
CTVHS
19 tháng 6 2023
\(\left(a\right):\left(x+y\right)^2-\left(x-y\right)^2=x^2+2xy+y^2-\left(x^2-2xy+y^2\right)\\ =x^2+2xy+y^2-x^2+2xy-y^2\\ =4xy\)
\(\left(b\right):\left(x-y-z\right)^2+\left(x+y+z\right)^2\\ =\left[\left(x-y\right)-z\right]^2+\left[\left(x+y\right)+z\right]^2\\ =\left(x-y\right)^2-2z\left(x-y\right)+z^2+\left(x+y\right)^2+2z\left(x+y\right)+z^2\\ =x^2-2xy+y^2-2xz+2yz+z^2+x^2+2xy+y^2+2xz+2yz+z^2\\ =2x^2+2y^2+2z^2+4yz\)
\(\left(c\right):\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\\ =\left[\left(x+y\right)-\left(x-y\right)\right]^2\\ =\left(x+y-x+y\right)^2\\ =\left(2y\right)^2=4y^2\)
25 tháng 10 2021
\(A=x^2-2xy+y^2+x^2+2xy+y^2+x^2-y^2=3x^2+y^2\\ B=\left(x-y-x+y-z\right)^2=\left(-z\right)^2=z^2\)
30 tháng 6 2019
\(a,\left(x+2\right)^2-\left(x-2\right)^2-2\left(x-2\right)\left(x+2\right).\)
\(=\left(x+2-x+2\right)^2=4^2=16\)
\(b,\left(x-y\right)^2+\left(x+y\right)^2+2\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y+x+y\right)^2=x^2\)
\(c,\left(x-y+z\right)^2-2\left(x+y\right)-2\left(x+y\right)\left(x-y\right)-z^2\)
4 tháng 7 2017
a,[x+y]^2.[x-y]^2=x4-2x2y2+y4
b,2.[x-y][x+y]+[x+y]^2+[x-y]^2=4x2
c,[x-y+z]^2+[z-y]^2+2.[x-y+z][y-z] (x - y + z)² + (z - y)² + 2(x - y + z)(y - z)
= (x - y + z)² + 2(x - y + z)(y - z) + (y - z)²
= (x - y + z + y - z)²
= x²
Câu c mk thấy khó nên viết luôn cách giải nha
CW
4 tháng 7 2017
a) \(\left(x+y\right)^2\cdot\left(x-y\right)^2=\left(x^2-y^2\right)^2\)
b) \(2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2+\left(x-y\right)^2=\left(x+y+x-y\right)^2=\left(2x\right)^2=4x^2\)
c) \(\left(x-y+z\right)^2+\left(z-y\right)^2+2\left(x-y+z\right)\left(y-z\right)=\left(x-y+z+y-z\right)^2=x^2\)
(Lấy y-z chứ không được lấy z-y)
DK
5 tháng 6 2021
Áp dụng BĐT phụ \(a^2+b^2\ge\dfrac{1}{2}\left(a+b\right)^2\Leftrightarrow\left(a-b\right)^2\ge0\)
\(A\ge\dfrac{1}{2}\left(x+y+\dfrac{1}{x}+\dfrac{1}{y}\right)^2\ge\dfrac{1}{2}\left(x+y+\dfrac{4}{x+y}\right)^2=\dfrac{1}{2}\left(1+\dfrac{4}{1}\right)^2=\dfrac{25}{2}\)
Dấu "=" \(x=y=\dfrac{1}{2}\)
