已知a,b满足(a+b)²=1,(a-b)²=25.(1)求a²+b²的值。(2)求ab的值

2025-02-23 17:40:13
推荐回答(3个)
回答1:

展开得:a2+2ab+b2=1 a2-2ab+b2=25,
两式相加得 2(a2+b2)=26,得a2+b2=13
两式相减得4ab=-24,得ab=-6

回答2:

a²+b²= [(a+b)²+(a-b)²]/2 = (1+25)/2 = 13
ab= [(a+b)²-(a-b)²]/4 = (1-25)/4 = -6

回答3:

13 -6