Question

Q.2) If (x + 1/x) = 3, then find the value of: a) (x² + 1/x²) and b) (x⁴ + 1/x⁴).​

Answer 1

Answer:

a)

${x}^{2} + \frac{1}{ {x}^{2} } = 7 \\\\\\b)\\ \\\:\: {x}^{4} + \frac{1}{ {x}^{4} } = 47$

Step-by-step explanation:

$x + \frac{1}{x} = 3 \\ \\ {(x + \frac{1}{x})}^{2} = 9 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 7 \\ \\ \\ \\ {( {x}^{2} + \frac{1}{ {x}^{2} })}^{2} = {7}^{2} \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 49 \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } = 49 - 2 \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } = 47$