Question

If x+ 1/x = 110. Then find x^3 + 1/x^3

Answer 1

x+ 1/x = 110
=> (x+1/x)^2 = 12100
=> x^2 + 1/x^2 +2*x*1/x = 12100
=> x^2 + 1/x^2 + 2 = 12100
=> x^2 + 1/x^2 = 12098 ---------(1)

Now,
x^3 + 1/x^3 = (x+1/x) (x^2 +1/x^2 - x*1/x)
= 110 * (12098 - 1) from equation 1
= 110 * 12097
= 1330670

Answer 2

HELLO DEAR,

GIVEN THAT:-
$x + \frac{1}{x} = 110$
TAKE CUBE BOTH SIDE

$(x + \frac{1}{x} )^{3} = {110}^{3} \\ = > {x}^{3} + ( { \frac{1}{x} })^{3} \times 3x \times \frac{1}{x} (x + \frac{1}{x} ) = 1331000\\ = > {x}^{3} + { \frac{1}{x} }^{3} + 3 \times 110 = 1331000 \\ = > {x}^{3} + ( { \frac{1}{x} })^{3} = 1331000 - 330 \\ = > 1330670$
I HOPE ITS HELP YOU DEAR,
THANKS