Question

If x-¹/x=4,then find the value of x+¹/x
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Answer 1

Answer:

1/4

is the correct answer for the question

Answer 2

Step-by-step explanation:

We have,

$\sf{x-\frac{1}{x}=4}$

$\sf{\implies{\frac{x^{2}-1}{x}=4}}$

$\sf{\implies{x^{2}-1=4x}}$

$\sf{\implies{x^{2}-4x-1=0}}$

Using quadratic formula,

$\boxed{\sf{x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}}}$

$\sf{\implies{x=\frac{4\pm\sqrt{4^{2}+4}}{2}}}$

$\sf{\implies{x=2\pm \sqrt{5}}}$

$\sf{\implies{x=2+ \sqrt{5}}}$

or,

$\sf{x=2-\sqrt{5}}$

Hence substituting the value of x,

we get,,

$\sf{x+\frac{1}{x}}$

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

$\sf{=\frac{(4+\sqrt{5})^{2}+1}{4+\sqrt{5}}}$

$\sf{\boxed{=\frac{8\sqrt{5}+22}{4+\sqrt{5}}}}$

Similarly you can see for 4-√5...

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