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Quantitative Aptitude

If | b | ≥ 1 ...

Question

$I f | b | \geq 1$ and x = - |a| b, then which one of the following is necessarily true?

A

a - x b < 0

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B

a - x b \geq 0

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C

a - x b > 0

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D

a - x b \leq 0

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Solution

The correct option is C $a - x b \geq 0$
$| b | \geq 1 \Rightarrow b \geq 1 o r b \leq - 1$
x = - |a| b (given)
Consider a - xb = a - (-|a|b)b
$= a + | a | b^{2} \geq 0$ since, $b^{2} \geq 1$

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Q. Prove that:

(i)

\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1

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