Question

if x^2+1/x^2=6. find X+1/x​

Answer 1

Answer:

given

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

we know that

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$then

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

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

${(x + \frac{1}{x} )}^{2} = 8 = {2}^{3}$

$\sqrt{ {(x + \frac{1}{x} )}^{2} } = \sqrt{ {8}^{3} }$

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

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