Question

if x+1/x=5, then x^+1/x^​

Answer 1

Step-by-step explanation:

We have ,x- 1/x=5

Then x-1=5x

5x-x=-1

4x=-1

X=-1/4

Now we have the value of x

X^2-1/x^2=(-1/4)^2-1/(-1/4)^2=(1/16)-1/( 1/16)

(-15/16) × 16/1= -15

Answer 2

Answer:

$$\begin{lgathered}(x + \frac{1}{x} ) {}^{2} = {(5)}^{2} \\ \\ {(x + \frac{1}{x} )}^{2} = {x}^{2} + \frac{1}{{x}^{2} } + 2 \\ \\ {(5)}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ 25 - 2 = {x}^{2} + \frac{1}{ {x}^{2} } \\ \\ 23 = {x}^{2} + \frac{1}{ {x}^{2} } \\ \\ \\ \\ (x - \frac{1}{x} ) {}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \\ \\ (x - \frac{1}{x} ) {}^{2} = 23 - 2 \\ \\ (x - \frac{1}{x} ) {}^{2} = 21 \\ \\ (x - \frac{1}{x} ) = \sqrt{21} \\ \\\end{lgathered}$$

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