Question

let's find the value of a²+1/a² when a-1/a=4​

Answer 1

Given:

• As given in the question,a -1/a = 4

To Find:

• Find the value of a^2 +1/a^2 = ?

Solution:

As given in the question, the value of a -1/a = 4 is given and we are said to find a^2 +1/a^2 and as we know the formula so let's find !

Using formula

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

Now substitute the values to get the result

$\: \: \sf \: ( {a}^{2} + \frac{1}{ {a}^{2} } ) = ( {a - \frac{1}{a} )}^{2} + 2. \cancel a .\frac{1}{ \cancel a} \\ \\ \\ \: \: \: \sf \: = {(4)}^{2} + 2 \\ \\ \\ \: \: \: \sf \: = 16 + 2 \\ \\ \\ \: \: \: \sf \dagger \therefore 18$

$\therefore$

Hence, the value of a^2 +1/a^2 is 18.

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