Ta có: \(\left(x-y\right)^2\ge0\)
=>\(x^2-2xy+y^2\ge0\)
=>\(x^2+y^2\ge2xy\)
=>\(x^2+y^2+x^2+y^2\ge2xy+x^2+y^2\)
=>\(2.\left(x^2+y^2\right)\ge\left(x+y\right)^2\)
=>\(x^2+y^2\ge\frac{1}{2}.\left(x+y\right)^2\)
=>ĐPCM
Ta có:
(x-y)2 >= 0
=> x2+y2 >= 2xy
<=> (x2+y2)*2 >= x2+y2+2xy=(x+y)2
<=> x2+y2 >= 1/2 (x+y)2