Question

solved question number 6 a b

Answer 1

Answer :

a : 7 b : 47

step - by - step explanation

$x + \frac{1}{x} = 3 \\ \\ \\ {(x + \frac{1}{x} )}^{2} = {3}^{2} \\ \\ \\ {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 9 \\ \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 7 \\ \\ \\ {(x + \frac{1}{x}) }^{4} = {3}^{4} \\ \\ \\ {x}^{4} + 4( {x}^{3} )( \frac{1}{x} ) + 6( {x}^{2} )( \frac{1}{ {x}^{2} }) + 4(x)( \frac{1}{ {x}^{3} } ) + \frac{1}{ {x}^{4} } = 81 \\ \\ \\ {x}^{4} + 4 {x}^{2} + 6 + 4 \frac{1}{ {x}^{2} } + \frac{1}{ {x}^{4} } = 81 \\ \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 4( {x}^{2} + \frac{1}{ {x}^{2} } = 75 \\ \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 4 \times 7 = 75 \\ \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 28 = 75 \\ \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } = 47$

thank you.