\(2\left(x^2+y^2\right)=\left(x+y\right)^2\)
\(\Rightarrow2x^2+2y^2=x^2+2xy+y^2\)
\(\Rightarrow x^2-2xy+y^2=0\)
\(\Rightarrow\left(x-y\right)^2=0\)
\(\Rightarrow x-y=0\Rightarrow x=y\)
\(\Rightarrowđpcm\)
Vậy...
\(2\left(x^2+y^2\right)=\left(x+y\right)^2\)
\(\Rightarrow2x^2+2y^2=\left(x+y\right)\left(x+y\right)\) (do lớp 7 nên mình chưa áp dụng hằng đẳng thức nha!)
\(\Rightarrow2x^2+2y^2=x^2+xy+xy+y^2\)
\(\Rightarrow2x^2+2y^2-x^2-y^2=2xy\)
\(\Rightarrow x^2-2xy+y^2=0\)
\(\Rightarrow x^2-xy-xy+y^2=0\)
\(\Rightarrow x.\left(x-y\right)-y.\left(x-y\right)=0\)
\(\Rightarrow\left(x-y\right)^2=0\Rightarrow x-y=0\)
\(\Rightarrow x=y\)(đpcm)
Chúc bạn học tốt!!!
