Question

If.... `a/b + b/a = 10` And... `a^2/b^2 + b^2/a^2 = 98` Find... `a^3/b^3 + b^3/a^3` Also can anyone find a formula to generate higher powers??

Answer 1

`970`

Explanation:

.

`a/b+b/a=10`

`(a^2+b^2)/(ab)=10`

`a^2+b^2=10ab`

`a^2/b^2+b^2/a^2=98`

`(a^4+b^4)/(a^2b^2)=98`

`a^4+b^4=98a^2b^2`

`a^3/b^3+b^3/a^3=(a^6+b^6)/(a^3b^3)=((a^2+b^2)(a^4-a^2b^2+b^4))/(a^3b^3)=`

`(10ab(98a^2b^2-a^2b^2))/(a^3b^3)=(10ab(97a^2b^2))/(a^3b^3)=(970a^3b^3)/(a^3b^3)=970`