Question

If x+√15=4 then x+1/x=? give the answer with proof

Answer 1

hey here your answer

Answer 2

x + √15 = 4

x = 4 - √15      -------: ( 1 )

$\dfrac{1}{4- \sqrt{15}}=\dfrac{1}{x}$

          By Rationalization

$\dfrac{1}{4-\sqrt{15}} \times \dfrac{4+\sqrt{15}}{4+\sqrt{15}} =\dfrac{1}{x}$

$\dfrac{4+\sqrt{15}}{(4)^{2} - (\sqrt{15})^{2}} = \dfrac{1}{x}$

$\dfrac{4+ \sqrt{15}}{16-15} = \dfrac{1}{x}$

$4 + \sqrt{15} = \dfrac{1}{x}\:\:\:\:\:\:\:\bold{-----:(1)}$

  Adding 1 & 2

4 - √15 + 4 + √15 = $x+\dfrac{1}{x}$

8 = $x+\dfrac{1}{x}$

Therefore the value of $x+\dfrac{1}{x}$ is 8.