Question

if x+1/x=5, find the value of x³+1/x³​

Answer 1

Answer :

https://brainly.in/question/4934762

Answer 2

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

/* By Algebraic Identity */

$\boxed{\pink{ a^{3}-b^{3} = (a-b)^{3} - 3ab(a-b)}}$

$\red{ Value \:of \: x^{3} + \frac{1}{x^{3} }}$

$= \Big( x - \frac{1}{x}\Big)^{3} + 3\times x \times \frac{1}{x} \Big( x - \frac{1}{x}\Big)$

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

$= 5^{3} + 3 \times 5 \: [ From \: (1) ]$

$= 125 + 15$

$= 140$

Therefore.,

$\red{ Value \:of \: x^{3} + \frac{1}{x^{3} }} \green { = 140 }$

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