Question

without solving explain why the equations do not have solutions​

Answer 1

Examining the equation

We have 2 terms:

$\sqrt{x+2}$ and $\sqrt{4x+1}$

For the sum of these to equal a negative number, in this case -3, one of these terms would have to be negative.

So what's the problem?

The function $\sqrt{x}$ (square root of x) only returns positive values!

(See the attached image for a graph of $\sqrt{x}$)

Since neither of the terms can be negative, it can't be equal to -3. In other words, no matter what we put as $x$, we can't solve the solution, so we say that the equation does not have any solutions.