Question

.If = (3 + √8) then find the value of
${x}^{2} + \frac{1}{ {x}^{2} }$
​

Answer 1

$\boxed{AnswEr}$

$\sf \ {x}^{2} + \frac{1}{ {x}^{2} } = 34$

★GivEn :-

• $\sf \: x = (3 + \sqrt{8} )$

★ To Find :-

• $\sf \: The \: Value \: of \: x^2 + \frac{1}{ {x}^{2} }$

$\boxed{Solution}$

1st Step :

$\sf \: x = (3 + \sqrt{8} ) \\ \sf \: or \: \: \: \: \: \frac{1}{x} = \frac{1}{(3 + \sqrt{8} )} \\ \sf \: or \: \: \: \frac{1}{x} = \frac{(3 - \sqrt{8} )}{(3 + \sqrt{8)}(3 - \sqrt{8} ) } \\ \sf \: or \: \: \frac{1}{x} = \frac{(3 - \sqrt{8} )}{(9 - 8)} = (3 - \sqrt{8)}$

2nd Step :

$\sf \: x + \frac{1}{x} \\ \sf \: = (3 + \sqrt{8} ) + (3 - \sqrt{8} ) \\ \sf \: = 3 + \sqrt{8} + 3 - \sqrt{8} = 6$

3rd Step :

$\sf \: {x}^{2} + \frac{1}{ {x}^{2} } \\ = \sf \: (x + \frac{1}{x} )^{2} - 2 \times x \times \frac{1}{x} \\ \sf \: = {6}^{2} - 2 = 36 - 2 = 34$

$\sf \therefore \: The \: answer \: is \: 34$

Answer 2

Answer:

34

hope it's helpful . . .

mark me as brainliest . . .