已知a+b=1,a(a平方+2b)+b(-3a+b平方)=0.5,求ab的值

2025-01-05 04:06:05
推荐回答(1个)
回答1:

a(a²+2b)+b(-3a+b²)=0.5
=a³+2ab-3ab+b³=0.5
=a³+b³-ab=0.5
=(a+b)(a²-ab+b²)-ab=0.5
∵a+b=1
∴a²-ab+b²-ab=0.5
=a²-2ab+b²=0.5
=(a+b)²-2ab-2ab=0.5
(a+b)²-4ab=0.5
∵a+b=1
∴1-4ab=0.5
-4ab=-0.5
ab=1/8