Question

if x square +1/x square equal to 25 find x+x/1

Answer 1

Your question needs a correction,


Correct question : Find the value of x + 1 / x





$\mathbf{Then, \: Solution : } \\ \\ \\ \\ Given, {x}^{2} + \frac{1}{ {x}^{2} } = 25$


Add 2( x × 1 / x ) on both sides,


${x}^{2} + \frac{1}{ {x}^{2} } + 2(x \times \frac{1}{x} ) = 25 + 2(x \times \frac{1}{x} )$





$We know, x^{2}+ \frac{1}{x^{2}} + 2( x \times \frac{1}{x} ) = {(x + \frac{1}{x} )}^{2}$




Hence,



$(x + \frac{1}{ x})^{2} = 25 + 2 \\ \\ \\ => {(x + \frac{1}{x}) }^{2} = 27 \\ \\ => x + \frac{1}{x} = \sqrt{27} \\ \\ \\ \\ => \bold{x + \frac{1}{x} = 3 \sqrt{3} }$