Question

if × -1/x=3 find x²+1/x² and x⁴ + 1/x²​

Answer 1

Step-by-step explanation:

$x - \frac{1}{x } = 3 \\ \\ = >( x - \frac{1}{x} ) ^{2} = 9 \\ \\ = > {x }^{2} + \frac{1}{ {x}^{2} } - 2.x. \frac{1}{x } = 9 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 11 \\ \\ = > ({x}^{2} + \frac{1}{ {x}^{2} } ) {}^{2} = 121 \\ \\ = > {x}^{4} + \frac{1}{ {x}^{4} } + 2. {x}^{2} . \frac{1}{ {x}^{2} } = 121 \\ \\ = > {x}^{4} + \frac{1}{ {x}^{4} } = 119$