Question

已知a+b=3,ab=½，求(1)a^4+b^4 (2)a分之b+b分之啊

已知a+b=3,ab=½，求(1)a^4+b^4 (2)a分之b+b分之a

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