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.