Question

if (a²+1/a²) =5 find (a⁴+1/a⁴) step by step solution​

Answer 1

ANSWER:—

(a²-1/a²)=5

whole square both side

(a²-1/a²)²=5²

a⁴+1/a⁴-2×a²×1/a²=25

a⁴+1/a⁴=27

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Answer 2

Question:

If (a²+ 1/a²) = 5 find (a⁴+ 1/a⁴)

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Given:

a² + 1/a² = 5

To find:

The value of a⁴+ 1/a⁴

Solution:

We have,

${a}^{2} + \frac{1}{ {a}^{2} } = 5$

Squaring both sides

$( {a}^{2} + \frac{1}{ {a}^{2} }) {}^{2} = (5) {}^{2} \\ \\ using \: identity \: (x + y) {}^{2} = {x}^{2} + {y}^{2} + 2xy \\ \\ \implies \: ( {a}^{2} ) {}^{2} + (\frac{1}{ {a}^{2} } ) {}^{2} + 2 \times a \times \frac{1}{a} = 25 \\ \\ \implies \: {a}^{4} + \frac{1}{ {a}^{4} } + 2 = 25 \\ \\ \implies \: {a}^{4} + \frac{1}{ {a}^{4} } = 2 5 - 2 \\ \\ \implies \: {a}^{4} + \frac{1}{ {a}^{4} } = 23$

Hence, the required value is 23.

Hope it helps you.