Question

已知a+b=3,ab=½,求(1)a^4+b^4 (2)a分之b+b分之啊

Answer 1

1,

a+b=3,

(a+b)²=9

a²+b²+2ab=9

a²+b²+2(1/2)=9,[ab=½,]

a²+b²=8

(a²+b²)²=8²

a^4+b^4+2a²b²=64

a^4+b^4+2(ab)²=64

a^4+b^4+2(1/2)²=64,[ab=½,]

a^4+b^4=127/2

2,

a分之b+b分之a

=b/a+a/b

=(b²+a²)/(ab)

=8/(1/2),[a²+b²=8,ab=½,]

=16