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SSC CGL 2020 PYQ — Question 68

SSC CGL - 7th March 2020 Shift 3 • Quantitative Aptitude • Q68

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If a4 + 1/a4 = 50, a > 0, then find the value of a3 + 1/a3.

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Correct answer: C

Explanation

The correct answer is option 3 i.e √[2(1 + √13)](-1 + 2√13)

Understanding Application
By the property, x2 + 1 / x2 = (x + 1 / x)2 - 2

We will put the value x = a2 in the given identity

⇒ (x4 + 1 / x4) = (x2 + 1 / x2)2 - 2

⇒ (x4 + 1 / x4) = (x2 + 1 / x2)2 - 2 = 50

⇒ (x4 + 1 / x4) = (x2 + 1 / x2)2 = 52

⇒ x2 + 1 / x2 = 2√13

⇒ (x + 1 / x)2 - 2 = 2√13

⇒ x + 1 / x = √(2√13 + 2)

⇒ x3 + 1 / x3 = (x + 1 / x)3 -3(x + 1 / x)

⇒ x3 + 1 / x3 = (√(2√13 + 2))3 -3(√(2√13 + 2))

⇒ ⇒ x3 + 1 / x3 = √[2(1 + √13)](-1 + 2√13)