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: \[ b = 5 \quad \text{or} \quad b = -5 \]