Question

已知(a+b)²=7,(a-b)²=4,求a²+b²和ab的值。

Answer 1

∵(a+b)²+(a-b)²=（a²+b²+2ab）+（a²+b²-2ab）=2a²+2b²=11

∴a²+b²=11/2

∵(a+b)²-(a-b)²=（a²+b²誉运+2ab）庆谈梁-（a²+b²-2ab）=a²侍世+b²+2ab-a²-b²+2ab=4ab=3
∴ab=3/4

Answer 2

(a+b)²毕岁+(a-b)²=a²+b²+2ab+a²+b²-2ab=2a²+2b²=11 ->a²+b²=11/耐皮2

(a+b)²昌数差-(a-b)²=a²+b²+2ab-a²-b²+2ab=4ab=3 -> ab=3/4