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SSC Selection Post 2022 PYQ — Question 70

SSC Selection Post - Matriculation Level - 05 Aug 2022 - Shift 3 • Quantitative Aptitude • Q70

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The mean propotional between (7+25)(7+2\sqrt5) and (21−65)(21-6\sqrt5) is:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 87\sqrt87.

Mean proportional = (7+25)(21−65)\sqrt{(7+2\sqrt5)(21-6\sqrt5)}

= (7+25)×3(7−25)\sqrt{(7+2\sqrt5) \times 3(7-2\sqrt5)}

= 3×(72−(25)2)=3×(49−20)=3×29=87\sqrt{3 \times (7^2 - (2\sqrt5)^2)} = \sqrt{3 \times (49 - 20)} = \sqrt{3 \times 29} = \sqrt{87}