Question

已知:(a+b)²=11,(a-b)²=5,则a²+b²的值等于_____

Answer 1

(a+b)²=11,得：a²+b²+2ab=11
(a-b)²=5，得：a²+b²-2ab=5
两式相加，得：2（a²+b²）=16
所以：a²+b²=8
已知:(a+b)²=11,(a-b)²=5,则a²+b²的值等于_8_

Answer 2

解：(a+b)²+(a-b)²=(a²+2ab+b²)+(a²-2ab+b²)=2(a²+b²）=16 所以a²+b²=8

Answer 3

(a+b)^2-(a-b)^2
=4ab
=11-5
=6
ab=3/2
a²+b²
=(a+b)^2-2ab
=11-3
=8