Question

If b is the mean proportion between a and c, then the mean proportion between (a² + b²) and (b² + c²) is ______.

Options

• a(b + c)

• b(a + c)

• c(a + b)

• none of these

Answer 1

If b is the mean proportion between a and c, then the mean proportion between (a² + b²) and (b² + c²) is b(a + c).

Explanation:

The mean proportion is `sqrt((a^2 + b^2)(b^2 + c^2))`.

Using b² = ac, this becomes `sqrt(a(a + c)c(a + c)) = b(a + c)`.