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If r and s are variables such that 1 /r^2 − 1 /s^2 > −9 and 2 /r^2 – 1

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If r and s are variables such that 1 /r^2 − 1 /s^2 > −9 and 2 /r^2 – 1 [#permalink]

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New post Updated on: 20 Nov 2017, 07:14
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If r and s are variables such that \(\frac{1}{r^2} − \frac{1}{s^2} > −9\) and \(\frac{2}{r^2} – \frac{1}{s^2} < 7\), which of the segments best represents the overlap zone for values of r and s?

1. \((-∞, − \frac{1}{4} ), (\frac{1}{4} , ∞)\)
2. \((− \frac{1}{4} , \frac{1}{4} )\)
3. \((-∞, − \frac{1}{5} ), (\frac{1}{5} , ∞)\)
4. \((− \frac{1}{4} , \frac{1}{4} )\)
5. \((-∞, − \frac{1}{5} ), (\frac{1}{4} , ∞)\)

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Originally posted by rahul16singh28 on 19 Nov 2017, 23:42.
Last edited by chetan2u on 20 Nov 2017, 07:14, edited 1 time in total.
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Re: If r and s are variables such that 1 /r^2 − 1 /s^2 > −9 and 2 /r^2 – 1 [#permalink]

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[quote="rahul16singh28"]If r and s are variables such that 1 /r^2 − 1 /s^2 > −9 and 2 /r^2 – 1/s^2 −9[/m]....(i)

\(\frac{2}{r^2} – \frac{1}{s^2} -7\)

now add (i) to it..
\(\frac{1}{s^2} – \frac{2}{r^2}+\frac{1}{r^2} − \frac{1}{s^2} > -7-9.....................\frac{-1}{r^2}>-16........\frac{1}{r^2}\frac{1}{16}\)
so \(r>\frac{1}{4}\)or \(r −9\)....(i)
multiply (i) by 2
\(\frac{2}{r^2} – \frac{2}{s^2} > -18\)

\(\frac{2}{r^2} – \frac{1}{s^2} -7\)

now add (i) to it..
\(\frac{1}{s^2} – \frac{2}{r^2}+\frac{2}{r^2} − \frac{2}{s^2} > -7-18.....................-\frac{1}{s^2}>-25........\frac{1}{r^2}\frac{1}{25}\)
so \(r>\frac{1}{5}\)or \(r\frac{1}{4}\) and \(s>\frac{1}{5}\)...... so overlap will be from HIGHER of 1/4 and 1/5 till infinity so \((\frac{1}{4},∞)\)

ans A

NOTE - rahul16singh28, pl use proper mathematical formula, it will be much easier to comprehend. Doing it 4 u.

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Re: If r and s are variables such that 1 /r^2 − 1 /s^2 > −9 and 2 /r^2 – 1   [#permalink] 20 Nov 2017, 07:06
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