Question

(x+1/x)=5 find x³+1/x³​

Answer 1

Answer:

110

Step-by-step explanation:

$x+\frac{1}{x}=5\\ Cubing\ both\ sides\\(x+\frac{1}{x})^{3}=125\\x^{3} + \frac{1}{x^{3}}+3(x+\frac{1}{x} )\\x+\frac{1}{x})^{3}=125\\x^{3} + \frac{1}{x^{3}}+3.5\\x+\frac{1}{x})^{3}=125\\x^{3} + \frac{1}{x^{3}}+15=125\\x+\frac{1}{x^{3}}=125-15\\=110$

Answer 2

Answer:

110

Step-by-step explanation:

Given:

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

${(x + \frac{1}{x} )}^{3} = {5}^{3} (cubing \: on \: both \: sides)$

${x}^{3} + \frac{1}{ {x}^{3} } + 3(x + \frac{1}{ x} ) = 125$

${x}^{3} + \frac{1}{ {x}^{3} } + 3(5) = 125$

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

$= 110$