If (a+1/a)^2=3 and a>0,prove that a^3+1/a^3=0.
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a^3 +b^3 = a^2 - ab + b^2
(a^3+ 1/a^3) = ( a+ 1/a) ( a^2 -1 +1/a^2) (1) equation
it is given that
(a+1/a)^2 = 3
or
( a+ 1/a) = √3. (2) equation
Also
( a+ 1/a)^2 = 3
or - a^2 + 1/a^2 +2 =3
then ( transpose 2 to subtract 3)
a^2 + 1/a^2 = 3-2
a^2 + 1/a^2 = 1. (3) equation
putting 2 and 3 in 1 we have
a^3 +1/a^3 = √3 (1-1) = 0
so the answer is 0
hope it helps
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