Question

. If x = √5 + 2, then x- 1/x equals​

Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

x = √5 + 2

$\underline{\bf{Explanation\::}}$

Now, we get 1/x ;

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

[Using by Rationalization method]$\longrightarrow\tt{\sqrt{5} + 1 - \sqrt{5} -1}$

$\mapsto\tt{\dfrac{1}{\sqrt{5} + 2} \times \dfrac{\sqrt{5} -2}{\sqrt{5} -2} }$

$\mapsto\tt{\dfrac{\sqrt{5} -2}{(\sqrt{5})^{2} - (2)^{2}} \:\:\underbrace{\sf{using\:formula\:(a^{2} - b^{2})}}}$

$\mapsto\tt{\dfrac{\sqrt{5} -2}{5 -4}}$

$\mapsto\tt{\dfrac{\sqrt{5} -2}{1}}$

Now,

$\longrightarrow\tt{x-\dfrac{1}{x} }$

$\longrightarrow\tt{\sqrt{5} + 2 - \dfrac{\sqrt{5} -2}{1} }$

$\longrightarrow\tt{\sqrt{5} +2 - \sqrt{5} -2}$

$\longrightarrow\tt{\cancel{\sqrt{5} - \sqrt{5}} \cancel{+2 -2}}$

$\longrightarrow\bf{00}$

Thus,

The value of x-1/x will be 0 .