If #a/b - b/a =3# Then what is the value of #a^3/b^3 + b^3/a^3#?
3 Answers
Explanation:
Multiplying out by
Explanation:
Given:
#a/b-b/a = 3#
Squaring both sides, we get:
#a^2/b^2-2+b^2/a^2 = 9#
Transposing and adding
#13 = a^2/b^2+2+b^2/a^2 = (a/b+b/a)^2#
Note that:
#(a/b+b/a)^3 = a^3/b^3+3a/b+3b/a+b^3/a^3#
So:
#a^3/b^3+b^3/a^3 = (a/b+b/a)((a/b+b/a)^2-3)#
#color(white)(a^3/b^3+b^3/a^3) = (a/b+b/a)(13-3)#
#color(white)(a^3/b^3+b^3/a^3) = +-10sqrt(13)#
Explanation: