Question

If a = √5 - 2, then a -1/a is _______

Answer 1

Answer:

$\mathtt\pink{SOLUTION:-}$

$\mathtt{a = \sqrt{5} - 2}$

$\mathtt{ \frac{1}{a} = \frac{1}{ \sqrt{5} - 2 } \times \frac{ \sqrt{5} + 2}{ \sqrt{5} + 2} }$

$\mathtt{ \frac{1}{a} = \frac{ \sqrt{5} + 2}{ { (\sqrt{5} )}^{2} + {(2)}^{2} } }$

$\mathtt{ \frac{1}{a} = \frac{ \sqrt{5} + 2}{5 - 4} }$

$\mathtt{ \frac{1}{a} = \sqrt{5} + 2 }$

$\mathtt\pink{ = a - \frac{1}{a} }$

$\mathtt\pink{ = \sqrt{5} - 2 - (\sqrt{5} + 2)}$

$\mathtt\pink{ = \sqrt{5} - 2 - \sqrt{5} - 2 }$

$\mathtt\pink{ = - 2 - 2}$

$\mathtt\pink{ = - 4}$

$\mathtt{ \: ANSWER \: IS \: -4}$