Question

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

Answer 1

a(a平方+2b)+b(-3a+b平方)=0.5

a³+2ab-3ab+b³=0.5

a³-ab+b³=0.5

(a+b)(a²-ab+b²)-ab=0.5

a²+2ab+b²-4ab=0.5

(a+b)²-4ab=0.5

∴ab=1/8