if x - 1/x = root 3 then find x^3 - 1/x^3
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Answer:
Step-by-step explanation:
x - 1/x = sqrt(3)
Then (x - 1/x)^3 = (sqrt(3))^3
x^3 - 1/x^3 + 2*x*(1/x) ( 1/x - x) = 3^(3/2)
x^3 - 1/x^3 - 2 (x - 1/x) =3^(3/2)
x^3 - 1/x^3 - 2 (sqrt(3)) =3^(3/2)
x^3 - 1/x^3 =3^(3/2) + 2 (sqrt(3))
=3^3 * 3^(1/2) + 2 * 3^(1/2)
=3^(1/2) * (3^3 + 2)
=root(3) * (9+2)
=11 * root(3)
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