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Đề thế này hả e
\(\dfrac{2x-y}{x+y}=\dfrac{2}{3}\)
\(\Leftrightarrow3\left(2x-y\right)=2\left(x+y\right)\)
\(\Leftrightarrow6x-3y=2x+y\)
\(\Leftrightarrow4x=4y\)
\(\Leftrightarrow x=y\)
Vậy.....
\(\dfrac{2x-y}{x+y}=\dfrac{2}{3}\Leftrightarrow3\left(2x-y\right)=2\left(x+y\right)\)
\(\Leftrightarrow6x-3y=2x+2y\)
\(\Leftrightarrow4x=5y\)
\(\Leftrightarrow\dfrac{x}{y}=\dfrac{5}{4}\)
Vậy....
a làm lại nhé, nãy sai
Ta có: \(\left(xy+2016z\right)\left(yz+2016z\right)\left(zx+2016y\right)\\ =\left(xy+\left(x+y+z\right)z\right)\left(yz+\left(x+y+z\right)x\right)\left(zx+\left(x+y+z\right)y\right)\\ =\left(xy+zx+zy+z^2\right)\left(yz+x^2+xy+xz\right)\left(zx+xỹ+y^2+yz\right)\\ =\left(y+z\right)\left(x+z\right)\left(x+z\right)\left(y+x\right)\left(z+y\right)\left(x+y\right)\\ =\left(y+z\right)^2\left(x+y\right)^2\left(z+x\right)^2\\ \Rightarrow\frac{\left(xy+2016z\right)\left(yz+2016z\right)\left(zx+2016y\right)}{\left(x+y\right)^2\left(y+z\right)^2\left(z+x\right)^2}\\ =\frac{\left(y+z\right)^2\left(x+y\right)^2\left(z+x\right)^2}{\left(x+y\right)^2\left(y+z\right)^2\left(z+x\right)^2}\\ =1\)
Ta có : \(x^4-7x^2+y^2+16=2xy\)
=> \(\left(x^2-8x^2+16\right)+\left(x^2-2xy+y^2\right)=0\)
=> \(\left(x-4\right)^2+\left(x-y\right)^2=0\)
Vì \(\left(x-4\right)^2\ge0 \forall x ,\left(x-y\right)^2 \ge0 \forall x,y \)
=> \(\left(x-4\right)^2+\left(x-y\right)^2\ge0 \forall x,y\)
=> \(\hept{\begin{cases}x-4=0\\x-y=0\end{cases}\Rightarrow\hept{\begin{cases}x=4\\x=y=4\end{cases}}}\)
Thay vào \(A=4^{2016}.4^{2017}-4^{2017}.4^{2016}+4+4=8\)
Vậy A=8
a, TK:
(x lẻ do \(2y^2-8y+3=2\left(y^2-4y\right)+3=x^2\) lẻ)
\(b,\Leftrightarrow\left(x^2-4x+4\right)+\left(y^2+4y+4\right)=9\\ \Leftrightarrow\left(x-2\right)^2+\left(y+2\right)^2=9\)
Vậy pt vô nghiệm do 9 ko phải tổng 2 số chính phương
\(A=\frac{\left(xy+2016z\right)\left(yz+2016x\right)\left(zx+2016y\right)}{\left(x+y\right)^2\left(y+z\right)^2\left(z+x\right)^2}\)
Thay \(x+y+z=2016\)
\(A=\frac{\left[xy+\left(x+y+z\right)z\right]\left[yz+\left(x+y+z\right)x\right]\left[zx+\left(x+y+z\right)y\right]}{\left(x+y\right)^2\left(y+z\right)^2\left(z+x\right)^2}\)
\(A=\frac{\left[xy+xz+yz+z^2\right]\left[yz+xy+xz+x^2\right]\left[zx+xy+yz+y^2\right]}{\left(x+y\right)^2\left(y+z\right)^2\left(x+z\right)^2}\)
\(A=\frac{\left[x\left(y+z\right)+z\left(y+z\right)\right]\left[y\left(z+x\right)+x\left(z+x\right)\right]\left[x\left(z+y\right)+y\left(z+y\right)\right]}{\left(x+y\right)^2\left(y+z\right)^2\left(x+z\right)^2}\)
\(A=\frac{\left[\left(y+z\right)\left(x+z\right)\right]\left[\left(x+z\right)\left(x+y\right)\right]\left[\left(z+y\right)\left(x+y\right)\right]}{\left(x+y\right)^2\left(y+z\right)^2\left(x+z\right)^2}\)
\(A=\frac{\left(x+z\right)\left(x+z\right)\left(y+z\right)\left(y+z\right)\left(x+y\right)\left(x+y\right)}{\left(x+y\right)^2\left(y+z\right)^2\left(x+z\right)^2}\)
\(A=\frac{\left(x+z\right)^2\left(y+z\right)^2\left(x+y\right)^2}{\left(x+y\right)^2\left(y+z\right)^2\left(x+z\right)^2}\)
\(A=1\)
Ta có
2x2 + y2 + 4 = 4x + 2xy
<=> (x2 - 4x + 4) + (x2 - 2xy + y2) = 0
<=> (x - 2)2 + (x - y)2 = 0
<=> x = y = 2
=> A = x2016.y2017 - x2017.y2016 + 36xy
= 22016.22017 - 22017.22016 + 36.2.2
= 144