The mean proportional between two positive numbers is 30. If the difference between the two numbers is 45, what is the smaller of the two numbers?
15
If the mean proportional between two numbers \(a\) and \(b\) is 30, then \(\sqrt{ab} = 30\), so \(ab = 900\).
The difference is \(a - b = 45\), so \(a = b + 45\).
Substitute: \(b(b + 45) = 900 \Rightarrow b^2 + 45b - 900 = 0\).
Solve: \(b = \dfrac{-45 + \sqrt{45^2 + 4 \times 900}}{2} = \dfrac{-45 + \sqrt{5625}}{2} = \dfrac{-45 + 75}{2} = 15\).
Hence, the smaller of the two numbers is 15.
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Important Questions from Mean Proportional
- Find the mean proportional between 19 and 76.
- Find the mean proportional of 324 and 16.
- Find the mean proportional between 28 and 252.
- Find the mean proportional of 400 and 4.
- Find the mean proportional of 225 and 4.
