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??

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Answer 1 · 2017-11-26T21:08:55

#970#

.

#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#