Question

if x=√5+2,than x-1/x equals
pllz tell​

Answer 1

$\texttt{\textsf{\large{\underline{Solution}:}}}$

GIVEN –

$\tt \implies x = \sqrt{5} + 2$

We have to find out the value of x - 1/x

$\tt \implies \dfrac{1}{x} = \dfrac{1}{\sqrt{5} + 2}$

$\tt \implies\dfrac{1}{x} =\dfrac{1 \times ( \sqrt{5} - 2)}{(\sqrt{5} + 2)( \sqrt{5} - 2)}$

$\tt \implies\dfrac{1}{x} =\dfrac{1 \times ( \sqrt{5} - 2)}{(\sqrt{5})^{2} - (2)^{2} }$

$\tt \implies\dfrac{1}{x} =\dfrac{\sqrt{5} - 2}{5-4}$

$\tt \implies\dfrac{1}{x} =\sqrt{5} - 2$

So,

$\tt \implies x - \dfrac{1}{x} = \sqrt{5} + 2 - ( \sqrt{5} - 2)$

$\tt \implies x - \dfrac{1}{x} = \sqrt{5} + 2 -\sqrt{5} + 2$

$\tt \implies x - \dfrac{1}{x} =4$

$\texttt{\textsf{\large{\underline{Answer}:}}}$

• x - 1/x = 4