Question

If x=1/5-x and x is not equal to 5 , find x^3+1/x^3

Answer 1

$\bf \red{ {x}^{3} + \frac{1}{ {x}^{3} } = 110}$

Given:

• if $x = \frac{1}{5 - x}$ ; $x \neq5$

To find:

• Find the value of ${x}^{3} + \frac{1}{ {x}^{3} }$.

Solution:

Formula/Concept to be used:

1. ${x}^{3} + \frac{1}{ {x}^{3} } = \left( {x + \frac{1}{x} } \right)^{3} - 3 \left(x + \frac{1}{x} \right )$
2. $( {a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b)$

Step 1:

Find the value of $x + \frac{1}{x}$

As,

$x = \frac{1}{5-x}$

cross multiply

$5-x = \frac{1}{x}$

or

$\bf \red{x + \frac{1}{x} = 5}$

Step 2:

Find the value of ${x}^{3} + \frac{1}{ {x}^{3} }$

According to the formula;

${x}^{3} + \frac{1}{ {x}^{3} } = \left( {x + \frac{1}{x} } \right)^{3} - 3 \left(x + \frac{1}{x} \right )$

put value of x+1/x.

${x}^{3} + \frac{1}{ {x}^{3} } = {5}^{3} - 3 \times 5$

or

${x}^{3} + \frac{1}{ {x}^{3} } = 125 - 15$

or

${x}^{3} + \frac{1}{ {x}^{3} } = 110$

Thus,

$\bf \: {x}^{3} + \frac{1}{ {x}^{3} } = 110$

Learn more:

1) if x-1/x=8 find x3-1/x3 https://brainly.in/question/10705814

2) If x2+1/x2=83 find the value of x3-1/x3 https://brainly.in/question/1403212

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Answer 2

Answer:

Concept - Basic exponent

Given - $x=\frac{1}{5-x}$ and x is not equal to 5

Find - $x^{3} + \frac{1}{x^{3} }$

Step-by-step explanation:

In the question it is given that $x = \frac{1}{x-5}$

$x = \frac{1}{x-5} \\(x+\frac{1}{x} = 5)$ ... 1

Now, $x^{3} + \frac{1}{x^{3} }$

$= > x^{3} + \frac{1}{x^{3} }=(x+\frac{1}{x})^{3} -3 (x+\frac{1}{x})\\= > x^{3} + \frac{1}{x^{3} } = (5)^{3} - 3 * 5\\= > x^{3} + \frac{1}{x^{3} } =110$

Answer is 110

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