Question

If a=9-4√5 then find the value of √a-1\√9

Answer 1

Answer:

If x=9-4√5 then find √x-1/√x - 3558961. this help

Step-by-step explanation:

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{(a-\frac{1}{a})^{2}=320}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\red{\underline \bold{Given :}} \\ \tt: \implies a = 9 - 4 \sqrt{5} \\ \\ \blue{\underline \bold{To \: Find :}} \\ \tt: \implies( a - \frac{1}{a} )^{2} =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {(a - \frac{1}{a}) }^{2} = {a}^{2} + \frac{1}{ { a }^{2} } - 2 \times a \times \frac{1}{a}$

$\\ \tt: \implies {(a - \frac{1}{a}) }^{2} = {(9 - 4 \sqrt{5}) }^{2} + \frac{1}{(9 - 4 \sqrt{5} )^{2} } - 2 \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} = {9}^{2} + {(4 \sqrt{5}) }^{2} - 72 \sqrt{5} + \frac{1}{ {9}^{2} + {(4 \sqrt{5 }) }^{2} - 72 \sqrt{5} } - 2 \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} =81 + 80 - 72 \sqrt{5} + \frac{1}{81 + 80 - 72 \sqrt{5} } - 2$

$\tt: \implies {(a - \frac{1}{a}) }^{2} =161 - 72 \sqrt{5} + \frac{1}{161 - 72 \sqrt{5} } \times \frac{161 + 72 \sqrt{5} }{161 + 72\sqrt{5} } - 2$

$\tt: \implies {(a - \frac{1}{a}) }^{2} =161 - 72 \sqrt{5} + \frac{161 + 72\sqrt{5} }{ {161}^{2} - {(72 \sqrt{5}) }^{2} } - 2 \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} =161 - 72 \sqrt{5} + \frac{161 + 72 \sqrt{5} }{25921 - 25920} - 2 \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} =161 - 72 \sqrt{5} + 161 + 72 \sqrt{5} - 2 \\ \\ \tt: \implies {(a - \frac{1}{a}$