Question

if (x+ 1/ x) is 5 then value of (x×x+1/x×x) is​

Answer 1

Answer:

Algebra is a vast topic... And these sums are common in that...

Let's get into solving!

$x+\frac{1}{x}=5$

Then, we need to find:

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

Now,

$x+\frac{1}{x}=5$

Square on both sides.

$(x+\frac{1}{x})^{2} =5^{2}$

5²=25.... <-------You should be knowing this...

Well, $(x+\frac{1}{x})^{2}$ is in the form of $(a+b)^{2}=a^{2}+b^{2} +2ab$

So, $(x+\frac{1}{x})^{2} =25$  can be written as $x^{2}+\frac{1}{x}^{2}+2*x*\frac{1}{x}=25$

If you observe the equation carefully, $2*x*\frac{1}{x}$, $x$ and $\frac{1}{x}$ will get cancelled.

Thus, $2*x*\frac{1}{x}$ is equal to 2×1 which is equal to 1.

Thus,

$x^{2}+\frac{1}{x}^{2}+2*x*\frac{1}{x}=25$ can be written as

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

Transpose 2 to the other side.

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

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

We got the answer!

Any doubts... ask in the comments

HOPE THIS HELPS :D