Question

how to solve this
$x + \frac{1}{x} = 5$
$x {}^{3} + \frac{1}{x} {}^{3}$
then find the value of

Answer 1

x + 1/x = 5

On cubing both sides, we get

( x + 1/x)^3 = 5^3

=> x^3 + 1/x^3 + 3(x) (1/x)( x + 1/ x) = 125

=> x^3 + 1/x^3 + 3 ( x + 1/x) = 125

=> x^3 + 1/x^3 + 3 (5) = 125

=> x^3 + 1/x^3 + 15 = 125

=> x^3 + 1/x^3 = 110

Answer 2

x + 1/x = 5

On cubing both sides, we get

( x + 1/x)^3 = 5^3

=> x^3 + 1/x^3 + 3(x) (1/x)( x + 1/ x) = 125

=> x^3 + 1/x^3 + 3 ( x + 1/x) = 125

=> x^3 + 1/x^3 + 3 (5) = 125

=> x^3 + 1/x^3 + 15 = 125

=> x^3 + 1/x^3 = 110