Question

x= 4-√15 then find the value of x-1/x =?​

Answer 1

GIVEN :-

• x = 4 - √15.

TO FIND :-

• The value of x - 1/x.

SOLUTION :-

Firstly let's calculate the value of 1/x,

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

On rationalising the denominator we get,

$\implies \sf \: \dfrac{1}{x} = \dfrac{1}{4 - \sqrt{15} } \times \frac{4 + \sqrt{15} }{4 + \sqrt{15} }$

$\implies \sf \: \dfrac{1}{x} = \dfrac{4 + \sqrt{15} }{4 ^{2} - \sqrt{15} ^{2} }$

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

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

Now According to the question,

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

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

$\implies \sf \: x - \dfrac{1}{x} = - \sqrt{15} - \sqrt{15}$

$\implies \underline{ \boxed{ \sf \: x - \dfrac{1}{x} = - 2 \sqrt{15} }}$

Answer 2

Given :-

x = 4 - √15

To Find :-

Value of x - 1/x

Solution :-

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

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

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

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

$\sf = 4 - \sqrt{15} - 4 - \sqrt{15}$

Cancelling 4

$\sf = -\sqrt{15} - \sqrt{15}$

$\sf = -2\sqrt{15}$