If \(x\) is the mean proportional between \((a+b)\) and \((a-b)\), then find the value of \(x\).
\(\sqrt{a^2 - b^2}\)
The mean proportional \(x\) between two numbers \(p\) and \(q\) satisfies: \(x^2 = p \times q\).
Here \(p = (a+b)\) and \(q = (a-b)\), so: \(x^2 = (a+b)(a-b)\).
Using the identity \((a+b)(a-b) = a^2 - b^2\): \(x^2 = a^2 - b^2\).
Therefore: \(x = \sqrt{a^2 - b^2}\).
Hence, the value of \(x\) is \(\sqrt{a^2 - b^2}\).
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Important Questions from Mean Proportional
What is the difference in the mean proportional between 1.8 and 3.2 and the third proportional to 5 and 3?
If x is subtracted from each of 23, 39, 32 and 56, the numbers so obtained, in this order, are in proportion. What is the mean proportional between (x + 4) and (3x + 1)?
When x is added to each of 9, 15, 21 and 31, the numbers so obtained are in proportion. What is the mean proportional between the numbers (3x - 2) and (5x + 4)?
When x is subtracted from each of 21, 22, 60 and 64, the numbers so obtained, in this order, are in proportion. What is the mean proportional between (x + 1) and (7x + 8)?
When x is subtracted from each of 19, 28, 55 and 91, the numbers so obtained in this order, are in proportion. What is the mean proportional between (x + 9) and x 2?
