Question

If 1/x = 3 - √8 the the value of x + 1/x is​

Answer 1

ANSWER:

• Value of the above expression is 6.

GIVEN:

$\implies \dfrac{1}{x} = 3 - \sqrt{8}$

TO FIND:

$value \: of \: x + \dfrac{1}{x}$

SOLUTION:

$\implies \dfrac{1}{x} = 3 - \sqrt{8} \\ \\ \implies \: x \: = \dfrac{1}{3 - \sqrt{8} } \\ \\ \implies \: x \: = \dfrac{1}{3 - \sqrt{8} } \times \dfrac{3 + \sqrt{8} }{3 + \sqrt{8} } \\ \\ \implies \: x = \dfrac{3 + \sqrt{8} }{(3) {}^{2} - ( \sqrt{8}) {}^{2} } \\ \\ \implies \: x = \dfrac{3 + \sqrt{8} }{9 - 8} \\ \\ \implies \: x \: = 3 + \sqrt{8} \\ \\ value \: of \: x + \dfrac{1}{x} \\ \\ = 3 + \sqrt{8} + 3 - \sqrt{8} \\ = 6$

Value of the above expression is 6.