Докажите тождество (х-у)^2+(x+y)^2=2(x^2+y^2)

просто открой квадраты: x^2 -2*x*y + y^2 + x^2 + 2*x*y +y^2= 2*x^2+2y^2=2(x^2+y^2) что и требовалось доказать...

 (х-у)²+(x+y)²=2(x²+y²) x²-2xy+y²+x²+2xy+y²=2x²+2y² 2x²+2y²=2x²+2y² ........................................................................................................................................................................................................................................................................  (х-у)²+(x+y)²=2(x²+y²) x²-2xy+y²+x²+2xy+y²=2x²+2y² 2x²+2y²=2x²+2y² ........................................................................................................................................................................................................................................................................  (х-у)²+(x+y)²=2(x²+y²) x²-2xy+y²+x²+2xy+y²=2x²+2y² 2x²+2y²=2x²+2y² ........................................................................................................................................................................................................................................................................