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SSC CHSL 2023 PYQ — Question 60

SSC CHSL 2023 - 03 Aug 2023 - Shift 3 • Quantitative Aptitude • Q60

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If a2+1a2=73{a^2}+\frac{1}{a^2}=\frac{7}{3}, then what is the value of a3−1a3{a^3}-\frac{1}{a^3}?

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Correct answer: B

Explanation

The correct answer is option 2 i.e.  1033\frac{10}{3\sqrt3}

Given that

If a2+1a2=73{a^2}+\frac{1}{a^2}=\frac{7}{3},

Calculation

⇒ (a - 1/a)2 + 2 = 7/3

⇒ (a - 1/a)2 = 7/3 - 2 = 1/3

⇒ a - 1/a = √(1/3)

Cubing both sides

⇒ a3−1a3{a^3}-\frac{1}{a^3} - 3 (a - 1/a) = (1/3)√(1/3)

⇒ a3−1a3{a^3}-\frac{1}{a^3} - 3 √(1/3) =  (1/3)√(1/3)

⇒ a3−1a3{a^3}-\frac{1}{a^3} =(10/3)√(1/3) =  1033\frac{10}{3\sqrt3}