# Find the value of x in the equation √ x + 5 = √ x + 45.

**Solution:**

The equation given in the problem statement is as follows:

\(\sqrt{x+5} = \sqrt{x+45 }\)

Squaring both sides we get

\((\sqrt{x+5})^{2} = (\sqrt{x+45})^{2}\)

x + 5 = x + 45

x will cancel on both sides

And we are left with

5 = 45

The above identity is false anyway and no inference that can be drawn from the above as the variable x is missing. Hence the algebraic expression has no solution.

It is further stated that a system of linear equations is said to be consistent if it has either one solution or infinitely many solutions; a system is** **inconsistent if it has no solution.

This seems to be the case of the equation given in the problem statement. It is inconsistent.

Hence the given equation has no solution.

## Find the value of x in the equation √ x + 5 = √ x + 45.

**Summary:**

The value of x in the equation √ x + 5 = √ x + 45 cannot be determined as the equation is inconsistent. Therefore there is no solution.

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