Question

Square root of (b squared -10 )squared =15

Answer 1

To solve the equation \(\sqrt{(b^2 - 10)^2} = 15\), we start by noting that the square root of a squared quantity can have two possibilities due to the properties of absolute values:

\[
|b^2 - 10| = 15
\]

This gives us two equations to solve:

1. \(b^2 - 10 = 15\)
2. \(b^2 - 10 = -15\)

Let's solve them one by one.

### For the first equation:
\[
b^2 - 10 = 15
\]
Adding 10 to both sides:
\[
b^2 = 25
\]
Taking the square root of both sides:
\[
b = 5 \quad \text{or} \quad b = -5
\]

### For the second equation:
\[
b^2 - 10 = -15
\]
Adding 10 to both sides:
\[
b^2 = -5
\]

Since the square of a real number cannot be negative, there are no real solutions from this equation.

### Final Solutions:
Thus, the only real solutions are:
\[
b = 5 \quad \text{or} \quad b = -5
\]