Multiple Choice Questions

What is x2 ab equal to x2 m2ab...........

Quantitative Aptitude (CDS) Algebra

Consider the following for next (02) two items that follows:

Let (x - a) (x - b) =    (x + a) (x + b)
(x - ma) (x - mb)     (x + ma) (x + mb)
m, a, b > 0.

What is x2 + ab equal to ?
x² + m²ab

This questions was previously asked in

2023 CDS -2 MATH

-1/m²

1/m²

2/m

1/m

- We need to solve the equation $\frac{(x - a) (x - b)}{(x + m a) (x + m b)} = \frac{(x + a) (x + b)}{(x + m a) (x + m b)}$ .

- Cross-multiplying gives $(x - a) (x - b) (x + m a) (x + m b) = (x + a) (x + b) (x + m a) (x + m b)$ .

- Simplifying both sides, we find symmetry: both sides are equal with $a$ replacing $- a$ and $b$ replacing $- b$ .

- The equation shows it holds true for specific conditions about $a$ , $b$ , and $m$ .

- We need $\frac{x^{2} + a b}{x^{2} + m^{2} a b}$ .

- Evaluate $\frac{x^{2} + a b}{x^{2} + m^{2} a b}$ , which simplifies to vary on $\frac{1}{m}$ .

Option 4 (1/m) is the correct answer.

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