Question

if x^4+1/x^4 = 34 (x > 1), then find the value of x +1/x​

Answer 1

Answer:

$( {x}^{2} + \frac{1}{ {x}^{2} } ) {}^{2} = {x}^{4} + \frac{1}{ {x}^{4} } + 2 \times x \times \frac{1}{ x}$

$( {x}^{2} + \frac{1}{ {x}^{2} } ) {}^{2} = 36$

${x}^{2} + \frac{1}{ {x}^{2} } = 6$

$(x + \frac{1}{x} ) {}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x}$

$(x + \frac{1}{x} ) = 8$

$(x + \frac{1}{x} ) = 2 \sqrt{2}$