Question

if x²+ 1/ x² =23 evaluate x+1/x​

Answer 1

Answer:

If $x$ is positive, then $x+\frac{1}{x}=5$. But if $x$ is negative, $x+\frac{1}{x}=-5$.

So, the answer could either be 5 or -5.

Step-by-step explanation:

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

Since we know that $x^2+\frac{1}{x^2} =23$, we can substitute to get:

$(x+\frac{1}{x})^2=23+2$

Simplifying the right hand side gives:

$(x+\frac{1}{x})^2=25$

We can now take the square root of both sides to get that:

$x+\frac{1}{x}=5$ or $x+\frac{1}{x}=-5$.

You didn't give enough information to tell which one, though. :)

Footnote

If we know that $x$ is positive, then we can deduce that $x+\frac{1}{x}$ would also be positive, so the answer would've been just 5.

If we know that $x$ is negative, then we can deduce that $x+\frac{1}{x}$ would also be negative, so the answer would've been just -5.

Hope this helps, and let me know if you have any further questions! :)