Question

If a²-3a -1 =0,find a²+1/a²​

Answer 1

Answer:

I don't know m nahi janta hu

Answer 2

Answer:

Given,

$\: \: \: \: \: \: \: \sf \: {a}^{2} - 3a - 1 = 0 \\ \sf \implies \: {a}^{2} - 1 = 3a \\ \sf \implies \: \frac{ {a}^{2} - 1 }{a} = 3 \\ \sf \implies \: \frac{ {a}^{2} }{a} - \frac{1}{a} = 3 \\ \sf \implies \: a - \frac{1}{a} = 3 \: \: \: \: \: \: - - - - (1)$

Now,

we know that,

${a}^{2} + {b}^{2} = {(a - b)}^{2} + 2ab$

So,

$\sf \: {a}^{2} + \frac{1}{ {a}^{2} } = {(a - \frac{1}{a} })^{2} + 2 \times \cancel a \times \frac{1}{ \cancel a} \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {3}^{2} + 2 \: \: \: \: \: \: \{ from \: eqn. \: (1)\} \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 9 + 2 \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 11$