Докажите тождество

1) a^2+b^2 = (a+b) ^2 + (a-b) ^2/2

2) (2a+b) ^2+b^2=2 (a^2 + (a+b) ^2)

3) (x/k) ^2 - (y/k) ^2 = 1/k^2 (x-y) (x+y)

4) (kx-ky) ^2=k^2 (x-y) ^2

Упрощаем правую часть:

1) ... = (a^2+2ab+b^2+a^2-2ab+b^2) / 2 = (2a^2+2b^2) / 2=a^2+b^2

2) ... = 2a^2+2 (a^2+2ab+b^2) = 2a^2+2a^2+4ab+2b^2=4a^2+4ab+2b^2 = (2a+b) ^2+b^2

3) ... = (x^2-y^2) / k^2=x^2/k^2-y^2/k^2 = (x/k) ^2 - (y/k) ^2

4) ... = (k (x-y)) ^2 = (kx-ky) ^2