已知a=（1-根号2）分之1,b=（1+根号2）分之1,求a的三次方*b+a*b的三次方的值

Question

已知a=（1-根号2）分之1,b=（1+根号2）分之1,求a的三次方*b+a*b的三次方的值

Answer 1

a=1/(1-√2)=-1/(√2-1)=-(√2+1)/[(√2+1)(√2-1)]=-√2-1
b=1/(1+√2)=(√2-1)/[(√2+1)(√2-1)]=√2-1
a+b=-√2-1+√2-1=-2
ab=-(√2+1)(√2-1)=-1
a³b+ab³
=ab(a²+b²)
=ab[(a+b)²-2ab]
=(-1)[(-2)²-2(-1)]
=-6