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SSC CGL 2020 PYQ — Question 79

SSC CGL Tier II - Quant - 16 Nov 2020 • Quantitative Aptitude • Q79

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The value of 7+353+5−7−353−5\frac{7 + 3\sqrt5}{3+\sqrt5} - \frac{7 - 3\sqrt5}{3-\sqrt5}  lies between:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 2 and 2.5

⇒ 7+353+5−7−353−5\frac{7 + 3\sqrt5}{3+\sqrt5} - \frac{7 - 3\sqrt5}{3-\sqrt5}

⇒ (7+35)(3−5)−(7−35)(3+5)(3+5)(3−5)\frac{(7 + 3\sqrt5)(3-\sqrt5) - (7 - 3\sqrt5)(3 + \sqrt5)}{(3 + \sqrt5)(3-\sqrt5)}

⇒ (6+25−6+254\frac{(6 + 2\sqrt5 - 6 + 2\sqrt5}{4}

 ⇒ 5\sqrt5 = 2.23