Question

Докажите тождество:
(a+b)²+(a-b)²=2(a²+b²)

a²+b²=(a+b)²-2ab

(a+b)²-(a-b)²=4ab

a²+b²=(a-b)²+2ab

Answer 1

1.(a+b)²+(a-b)²=2(a²+b²)
(a+b)²+(a-b)²=a²+2ab+b²+a²-2ab+b²=2a²+2b²=2(a²+b²
2.a²+b²=(a+b)²-2ab
(a+b)²-2ab=a²+2ab+b²-2ab=a²+b
3.(a+b)²-(a-b)²=4ab
(a+b)²-(a-b)²=a²+2ab+b²-a²=2ab-b²=4ab
4.a²+b²=(a-b)²+2ab
(a-b)²+2ab=a²-2ab+b²+2ab=a²+b²