If x is the harmonic mean between y and z, then which one of the following is correct?
- A. xy+xz-yz=0
- B. xy+xz-2yz=0 ✓
- C. xy+xz+yz=0
- D. xy+xz-4yz=0
Correct Answer: B. xy+xz-2yz=0
Explanation
Since x is the harmonic mean of y and z, \frac{2}{x} = \frac{1}{y} + \frac{1}{z}. This simplifies to \frac{2}{x} = \frac{y+z}{yz} \implies 2yz = x(y+z) = xy + xz. Rearranging gives xy + xz - 2yz = 0.
Related questions on Algebra
- If p + q + r = 0, then what is z^{\frac{p^2}{qr}} \times z^{\frac{q^2}{rp}} \times z^{\frac{r^2}{pq}} equal to ?
- What is the value of k for which (k^2 - 5k + 4)x^2 + (k^2 - 3k - 4)x + (k^2 - 4k) = 0 is an identity ?
- If \frac{a^2}{b^2 + c^2} = \frac{b^2}{c^2 + a^2} = \frac{c^2}{a^2 + b^2}, then what is the value of a^4 + b^4 + c^4 equal to ?
- If \frac{1}{x} = \frac{1}{p} + \frac{1}{q}, then what is \frac{pq}{p^2 - q^2}\left(\frac{x + p}{x - p} - \frac{x + q}{x - q}\right) equa...
- If (x - 5) is the HCF of x^2 - x - p and x^2 - qx - 10, then what is the value of (p + q) ?