Question

If a+1/a=8
Find a^6+1/a^6
Please help me

Answer 1

Answer:

$\bold\red{238142}$

Step-by-step explanation:

Given,

$a + \frac{1}{a} = 8$

Squaring both sides,

we get,

$= > ( {a + \frac{1}{a} )}^{2} = {8}^{2} \\ \\ = > {a}^{2} + \frac{1}{ {a}^{2} } + 2 = 64 \\ \\ = > {a}^{2} + \frac{1}{ {a}^{2} } = 64 - 2 = 62$

Now,

cubing both sides

we get,

$= > {( {a}^{2} + \frac{1}{ {a}^{2} } ) }^{3} = {(62)}^{3} \\ \\ = > {a}^{6} + \frac{1}{ {a}^{6} } + 3 \times {a}^{2} \times \frac{1}{ {a}^{2} } \times ( {a}^{2} + \frac{1}{ {a}^{2} } ) = {(62)}^{3} \\ \\ = > {a}^{6} + \frac{1}{{ a }^{6} } + 3 \times 62 = {(62)}^{3} \\ \\ = > {a}^{6} + \frac{1}{ {a}^{6} } = 238142$