Question

If (a/b+b/a)=1,then(a 3+b 3)=?

Answer 1

(a/b)+(b/a)=1
(a²+b²)/ab=1
a²+b²=ab


now..
a³+b³=(a+b)(a²-ab+b²)
=(a+b)(a²+b²-ab)
=(a+b)(ab-ab)
=(a+b)(0)
a³+b³=0

Answer 2

(a/b+b/a)=1
==>(a^2+b^2)/ab=1
==>a^2+b^2=ab
==>(a+b)^2=3ab
==>a+b=√(3ab)
==>3(a+b)=3√(3ab)