Question

If x ➖1 by x is equal to 5bfind x cube ➖1 by x cube

Pls help
Jo help karega vo fal payega Kya sabhi so gye hai kya koi help nhi karta meri

Answer 1

120

Step-by-step explanation:

Given:

$x + \dfrac{1}{x} = 5$

To find:

${x}^{3} + \dfrac{1}{{x}^{3} }$

How to Solve ?

1. As we need cube so we will cube both side.

2. Use Algebra Formula

3. Substitute the given value.

4. Simplify and get the answer ....

5. Very Simple ^_^ I understood.

Solution:

$x + \dfrac{1}{x} = 5$

[Cubing both side]

${(x + \frac{1}{x})}^{3} = {(5)}^{3} \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3.x. \frac{1}{x} (x + \frac{1}{x}) = 5 \times 5 \times 5 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3(x + \frac{1}{x} ) = 125 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3(5) = 125\: \: \: \: [\textsf{From given}] \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 125 - 15 \\ \\ \boxed{ {x}^{3} + \frac{1}{ {x}^{3} } = 120}$

Therefore, the required answer is 120.

Some Important Algebra Formula

${(x + y)}^{3}={x}^{3}+{y}^{3}+ 3xy(x + y) \\ \\(x - y)^{3}={x}^{3}-{y}^{3}- 3xy(x - y)$