Question

已知a^2=b+5,b^2=a+5(a≠b),求a^3-2ab+b^3的值

过程详细一点

Answer 1

a²=b+5
b²=a+5
两式相减
(a+b)(a-b)=-(a-b)
a+b=-1
两式相乘
(ab)²=ab+5(a+b)+25
(ab)²-ab-20=0
(ab-5)(ab+4)=0
解得ab=5或ab=-4
a³-2ab+b³
=(a+b)(a²-ab+b²)-2ab
=(a+b)[(a+b)²-3ab]-2ab
当ab=5时a³-2ab+b³=4
当ab=-4时a³-2ab+b³=-4