Question

If x2+1/x2=5 then find the value of x+1/x​

Answer 1

☯$\large\mathfrak \pink{Solution:-}$

☯$\underline \mathbb{GIVEN:-}$

${x}^{2} + \frac{1}{ {x}^{2} } = 5$

☯$\underline \mathbb{TO \: FIND:-}$

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

☯$\underline \mathbb{FORMULA:-}$

${(x + \frac{1}{ {x} } )}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times \cancel{x \times \frac{1}{x} } \\ \\ \implies \: {x}^{2} + \frac{1}{ {x}^{2} } + 2$

☯$\underline \mathbb{BY \: THE \: PROBLEM:-}$

${x}^{2} + \frac{1}{ {x}^{2} } = 5$

Add two in both the terms.

${x}^{2} + \frac{1}{ {x}^{2} } + 2 = 5 + 2 \\ \\ \implies \: {(x + \frac{1}{x} )}^{2} = 7 - - (By \: Formula)\\ \\ \implies \:(x + \frac{1}{x} ) = \sqrt{7}$

☯$\underline \mathbb{ANSWER:-}$

$\\ {\implies \boxed{\:(x + \frac{1}{x} ) = \sqrt{7}}}$