If \frac{p+q}{q+r} = \frac{r+s}{s+p}; (q+r) \neq 0, (s+p) \neq 0, then which one of the following is correct?
- A. p + q + r + s = 0
- B. p = r
- C. Either p + q + r + s = 0 or p = r ✓
- D. None of the above
Correct Answer: C. Either p + q + r + s = 0 or p = r
Explanation
Cross multiplying yields (p+q)(s+p) = (q+r)(r+s). Expanding gives ps + p^2 + qs + pq = qr + qs + r^2 + rs. Rearranging terms, p^2 - r^2 + ps + pq - qr - rs = 0, which factors into (p-r)(p+q+r+s) = 0. Hence, either p=r or p+q+r+s=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) ?