What is x equal to ?
Consider the following for the next two (02) items that follow : Let \frac{(x-a)(x-b)}{(x-ma)(x-mb)}=\frac{(x+a)(x+b)}{(x+ma)(x+mb)}; m, a, b \gt 0.
- A. \pm\sqrt{mab} ✓
- B. \pm\sqrt{ab}
- C. \pm\sqrt{2mab}
- D. \pm\sqrt{2ab}
Correct Answer: A. \pm\sqrt{mab}
Explanation
From the previous result, \frac{x^2+ab}{x^2+m^2ab} = \frac{1}{m}. Cross-multiplying gives m(x^2+ab) = x^2+m^2ab. Factoring out terms yields x^2(m-1) = mab(m-1). Since m, a, b \gt 0, this simplifies to x^2 = mab, or x = \pm\sqrt{mab}.
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