Question

X + 1 / X 1 x exponent 4 + 1 / x exponent 4 is equal to 194

Answer 1

${x}^{4} + \frac{1}{ {x}^{4} } = 194 \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 {x}^{2} \times \frac{1}{ {x}^{2} } = 194 + 2 {x}^{2} \times \frac{1}{ {x}^{2} } \\ {( {x}^{2} + \frac{1}{ {x}^{2} } ) }^{2} = 196 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 14 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 14 + 2 \\ {(x + \frac{1}{x}) }^{2} = 16 \\ x + \frac{1}{x} = 4$