Question

If x^2+1/x^2=51 then find x+1/x

Answer 1

Answer:

$x + \frac{1}{x} = \sqrt{53}$

Step-by-step explanation:

given equation

${x}^{2} + \frac{1}{ {x}^{2} } = 51$

find to

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

${(x + \frac{1}{x}) }^{2} = {x}^{2} + 2(x)( \frac{1}{x} ) + \frac{1}{ {x}^{2} } \\ \\ {(x + \frac{1}{x}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2(1) \\ \\ {(x + \frac{1}{x}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ {(x + \frac{1}{x}) }^{2} = 51 + 2 \\ \\ {(x + \frac{1}{x}) }^{2} = 53 \\ \\ x + \frac{1}{x} = \sqrt{53}$