Solve the following mathematical problems:

$i f a + \frac{1}{a} = 3, p r o v r t h a t a^{4} + \frac{1}{a^{4}} = 119$
(Algebra)

Created: 2 years ago | Updated: 1 year ago

Updated: 1 year ago

Answer :

$G i v e n t h a t, a + \frac{1}{a} = 3 L . H . S = a^{4} + \frac{1}{a^{4}} = {(a^{2})}^{2} + {(\frac{1}{a^{2}})}^{2} = (a^{2} + \frac{1}{a^{2}}) - 2 \times a^{2} \times \frac{1}{a^{2}} [∵ a^{2} + b^{2} = {(a + b)}^{2} - 2 a b] = {(a^{2} + \frac{1}{a^{2}})}^{2} - 2 = {{(a - \frac{1}{a})}^{2} + 2 \times a \times \frac{1}{a}}^{2} - 2 = {{(3)}^{2} + 2}^{2} - 2 = {(9 + 2)}^{2} - 2 = 11^{2} - 2 = 121 - 2 = 119 ∴ L . H . S . = R . H . S . (P r o v e d)$

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Question:
$i f a + \frac{1}{a} = 3, p r o v r t h a t a^{4} + \frac{1}{a^{4}} = 119$
(Algebra)

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