Question

solve the problem with correct solution​

Answer 1

8 kindly check the attachment

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{x + \sqrt{15} = 4}$

TO DETERMINE

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

EVALUATION

Here it is given that

$\displaystyle \sf{x + \sqrt{15} = 4}$

$\displaystyle \sf{ \implies \: x = 4 - \sqrt{15} }$

$\displaystyle \sf{ \implies \: \frac{1}{x} = \frac{1}{4 - \sqrt{15} } }$

$\displaystyle \sf{ \implies \: \frac{1}{x} = \frac{(4 + \sqrt{15} )}{(4 + \sqrt{15})( 4 - \sqrt{15}) } }$

$\displaystyle \sf{ \implies \: \frac{1}{x} = \frac{(4 + \sqrt{15} )}{ {4}^{2} - {( \sqrt{15} )}^{2} } }$

$\displaystyle \sf{ \implies \: \frac{1}{x} = \frac{(4 + \sqrt{15} )}{ 16 - 15} }$

$\displaystyle \sf{ \implies \: \frac{1}{x} = \frac{(4 + \sqrt{15} )}{ 1} }$

$\displaystyle \sf{ \implies \: \frac{1}{x} = 4 + \sqrt{15} }$

Therefore

$\displaystyle \sf{ \: x + \frac{1}{x} }$

$\displaystyle \sf{ = (4 - \sqrt{15} ) + (4 + \sqrt{15}) }$

$\displaystyle \sf{ = 8}$

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