若(a+b)²=8,(a-b)²=5,求a²+b²和ab的值

若(a+b)²=8,(a-b)²=5,求a²+b²和ab的值
若(a+b)²=8,(a-b)²=5,求a²+b²和ab的值

若(a+b)²=8,(a-b)²=5,求a²+b²和ab的值
(a+b)²+(a-b)² = 2(a²+b²)
所以(a²+b²) = (8+5)/2 = 13/2
(a+b)²-(a-b)² = 4ab
所以ab = (8-5)/4 = 3/4

(a+b)²+(a-b)² = 2(a²+b²)
所以(a²+b²) = (8+5)/2 = 13/2
(a+b)²-(a-b)² = 4ab
所以ab = (8-5)/4 = 3/4