Question

if a= 9-4 root 5 find the value of (a-1/a )^2 ​

Answer 1

$\huge\{\overbrace{\underbrace{\bold{\pmb{ \: \: \purple{answer} \: \: }}}}\}$

$({a - \frac{1}{a}) }^{2}$

Here a = 9 - 4_/5

$({9 - 4 \sqrt{5} - \frac{1}{9 - 4 \sqrt{5} } ) }^{2}$

$({1 - 72 \sqrt{5} - \frac{1}{9 - 4 \sqrt{5} }) }^{2}$

$( { \frac{ - 72 \sqrt{5} }{9 - 4 \sqrt{5} } )}^{2} = \frac{5184 \times 5}{9 - (16 - 5)}$

$\frac{25920}{2} = 12960$

Answer 2

Answer:

$\red{ \underline{ \mathfrak{given }} \colon\: a = 9 - 4 \sqrt{5} }\\ \blue{ {(a - \frac{1}{a} )}^{2} = {a}^{2} + \frac{1}{ {a}^{2} } - 2 \times a \times \frac{1}{a} }\\ \blue{ = {(9 - 4 \sqrt{5} )}^{2} + \frac{1}{ {(9 - 4 \sqrt{5} )}^{2} } - 2 }\\ \blue{ =( 81 + 80 - 72 \sqrt{5} ) + \frac{1}{(81 + 80 - 72 \sqrt{5})} - 2} \\ \blue{ = (161 - 72 \sqrt{5} ) + \frac{1}{(161 - 72 \sqrt{5} )} - 2 }\\ \blue{ = \frac{ {(161 - 72 \sqrt{5}) }^{2} + 1 - 2(161 - 72 \sqrt{5} ) }{(161 - 72 \sqrt{5} )} }\\ \blue{= \frac{25921 + 25920 - 23184 \sqrt{5} + 1 - 322 + 144 \sqrt{5} }{(161 - 72 \sqrt{5}) } } \\ \blue{= \frac{51520 - 23040 \sqrt{5} }{161 - 72 \sqrt{5} } } \\ \\ \red{\mathfrak{\underline{\large{hope \: it \: helps \: you }}}} \\ \green{\mathfrak{\underline{\large{mark \: me \: brainliest}}}}$