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

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 (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

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