Question

If x square + 1/x square=47, find the value of x+1/x​

Answer 1

Answer:

7

Step-by-step explanation:

${x}^{2} + { \frac{1}{ {x}^{2} } } = 47 \\ since \: {(x + \frac{1}{x}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ = > {(x + \frac{1}{x}) }^{2} = 47 + 2 \\ = > {(x + \frac{1}{x}) }^{2} = 49 \\ = > x + \frac{1}{x} = \sqrt{49} \\ = > x + \frac{1}{x} = 7$