Question

If a+1/a=2, find the value of a⁴+1/a⁴ Step by Step explaination is required​

Answer 1

$\red{a + \frac{1}{a} = 2} \\\\ {(a + \frac{1}{a} ) }^{2} = {a}^{2} + \frac{1}{ {a}^{2} } + 2 \times a \times \frac{1}{a} \\\\ {(2)}^{2} = {a}^{2} + \frac{1}{ {a}^{2} } + 2 \\\\ 4 = {a}^{2} + \frac{1}{ {a}^{2} } + 2 \\\\ {a}^{2} + \frac{1}{ {a}^{2} } = 4 - 2 \\\\ \red{ {a}^{2} + \frac{1}{ {a}^{2} } = 2} \\\\ {({a}^{2} + \frac{1}{ {a}^{2} } ) }^{2} = {a}^{4} + \frac{1}{ {a}^{4} } + 2 + {a}^{2} \times \frac{1}{ {a}^{2} } \\\\ {({a}^{2} + \frac{1}{ {a}^{2} } ) }^{2} = {a}^{4} + \frac{1}{ {a}^{4} } + 2 \\\\ {(2)}^{2} = {a}^{4} + \frac{1}{ {a}^{4} } + 2 \\\\ 4 = {a}^{4} + \frac{1}{ {a}^{4} } + 2 \\\\ {a}^{4} + \frac{1}{ {a}^{4} } = 4 - 2 \\\\ \red{{a}^{4} + \frac{1}{ {a}^{4} } = 2}$