If \(\dfrac{1}{b-a}+\dfrac{1}{b-c}=\dfrac{2}{b}\), then \(a, b\) and \(c\) are in
HP
Simplifying \(\dfrac{1}{b-a}+\dfrac{1}{b-c}=\dfrac{2}{b}\) leads to \(ab+bc=2ac\), which on dividing by \(abc\) gives \(\dfrac{1}{c}+\dfrac{1}{a}=\dfrac{2}{b}\). Thus \(\dfrac{1}{a}, \dfrac{1}{b}, \dfrac{1}{c}\) are in AP, so \(a, b, c\) are in HP.
Similar Questions
If H is the Harmonic Mean of three numbers 10C4, 10C5, and 10C6, then what is the value of \(\frac{270}{H}\) ?
If the roots of the equation a (b - c) x 2+ b (c - a) x + c (a - b) = 0 are equal, then which one of the following is correct?
If the harmonic mean of 60 and x is 48, then what is the value of x?
If H is the harmonic mean of numbers 1, 2, 22, 23, ......2n-1 what is n/H equal to ?
Important Questions from Harmonic Progressions
The nth terms of the two series 3 + 10 + 17 + ... and 63 + 65 + 67 + .... are equal, then the value of n is:
The value of n, for which \(\dfrac{a^{n+1} + b^{n+1}}{a^n+b^n}\) is the harmonic mean of a and b, is
Suppose that m and n are fixed numbers such that the mth term of an HP is equal to n and the nth term is equal to m, (m ≠ n). Then the (m + n)th term is:
If H is the Harmonic Mean of three numbers 10C4, 10C5, and 10C6, then what is the value of \(\frac{270}{H}\) ?
If the roots of the equation a (b - c) x 2+ b (c - a) x + c (a - b) = 0 are equal, then which one of the following is correct?
