Question

If $xϵR$, the number of solutions of $\sqrt{2x+1}-\sqrt{2x-1}-1$ is

• A. $1$
• B. $2$
• C. $4$
• D. $infinite$

Answer 1

The correct option is D $infinite$

We have,

$x\in R$

Then,

$\sqrt{2x+1}-\sqrt{2x-1}-1$

Now,

Put $x=1,2,3,\mathrm{4.........}$

So,

$\sqrt{2\left(1\right)+1}-\sqrt{2\left(1\right)-1}-1=\sqrt{3}-2$

$\sqrt{2\left(2\right)+1}-\sqrt{2\left(2\right)-1}-1=\sqrt{5}-\sqrt{3}-1$

And so on….

Then,

Infinite number of solution.

Hence, this is the answer.