Question

if x + one by X is equals to 4 find the value of x square + one by x square

Answer 1

X=1/3
1/9+3
1+27/9
28/9

Answer 2

✔️hey mate! here's your answer!✔️
____________________________

since,
$\\ x + \frac{1}{x} = 4$

also, we know that,

(a + b)² = a² + b² + 2ab

so, using this identity,
$\\ = > ( {x + \frac{1}{x} })^{2} = ( {x})^{2} + ( \frac{1}{x} )^{2} + 2(x \times \frac{1}{x} )$

then, substituting the value of x,
$\\ = > ( {4})^{2} = {x}^{2} + \frac{1}{x^{2}} + 2$
$\\ = > 16 = {x}^{2} + \frac{1}{ {x}^{2} } + 2$

then, take 2 to other side, and it is positive, so it will become negative.
$\\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2$
$\\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 14$

thus, your answer is 14.

hope you understood!