已知a=3+2(根号2),b=3-2（根号2）,求a分之b+b分之a的值和a^4-b^4,急啊,亲们,帮下忙啦,要快~~~

Question

已知a=3+2(根号2),b=3-2（根号2）,求a分之b+b分之a的值和a^4-b^4,急啊,亲们,帮下忙啦,要快~~~

Answer 1

a=3+2√2
b=3-2√2
ab=(3+2√2)(3-2√2)=1
所以 b/a+a/b
=(b²+a²)/ab
=b²+a²
=(3+2√2)²+(3-2√2)²
=2(9+8)
=34
a^4-b^4
=(a²+b²)(a²-b²)
=34(a-b)(a+b)
=34*4√2*6
=816√2