Question

Answer with clear process.

Answer 1

Given : a^4 + (1/a^4) = 322.

It can be written as,

⇒ a^4 + (1/a^4) = 324 - 2

⇒ a^4 + (1/a^4) + 2 = 324

⇒ (a^2 + 1/a^2)^2 = 324

⇒ (a^2 + 1/a^2) = √324

⇒ (a^2 + 1/a^2) = 18

Now,

It can be written as,

⇒ a^2 + (1/a^2) = 16 + 2

⇒ a^2 + (1/a^2) - 2 = 16

⇒ (a - 1/a)^2 = 16

⇒ a - (1/a) = 4,-4

Hope it helps!

Answer 2

$Given : {a}^{2} + \frac{1}{ {a}^{2} } = 322 \\ \\ To \: \: be \: \: found \\ \\ a - \frac{1}{a} = ? \\ \\ Solution \\ \\ {a}^{4} + \frac{1}{ {a}^{4} } = 322 \\ \\ = > {a}^{4} + \frac{1}{ {a}^{4} } + 2 = 322 + 2 \\ \\ = > {( {a}^{2} + \frac{1}{ {a}^{2} } )}^{2} = 324 \\ \\ = > {( {a}^{2} + \frac{1}{ {a}^{2} } )}^{2} = {(18)}^{2} \\ \\ = > ( {a}^{2} + \frac{1}{ {a}^{2} } ) = 18 \\ \\ = > ( {a}^{2} + \frac{1}{ {a}^{2} } ) - 2 = 18 - 2 \\ \\ = > {(a - \frac{1}{a} )}^{2} = 16 \\ \\ = > (a - \frac{1}{a} ) = 4 \: \: ,( - 4)$