Question

ifx+1/x=5 find the value of x³+1/x³

Answer 1

x+1/×=5
cubing both sides, we get
x^3+1/x^3+3×(x+1/x)=125
x^3+1/x^3+3(5)=125
x^3+1/x^3=125-15=110

Answer 2

Heya friend,
Here is the answer you were looking for:
$x + \frac{1}{x} = 5$

Cubing both the sides we get

${(x + \frac{1}{x} )}^{3} = {(5)}^{3}$

Using the identity :

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b)$

${(x)}^{3} + {( \frac{1}{x}) }^{3} + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) = 125 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3(5) = 125 \\ \\ {x}^{3} + \frac{1 }{ {x}^{3} } + 15 = 125 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 125 - 15 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 110$

Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
☺☺