SarkariPYQ

SSC CGL 2021 PYQ — Question 75

SSC CGL - 16 Aug 2021 - Shift 2 • Quantitative Aptitude • Q75

Back to paper

If 4x4 - 37x2 + 9 =0, x> √32\frac{3}{2},then what is the value of 8x3 -27x3\frac{27}{x^3}?

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 215

Given :

 4x4 - 37x2 + 9 =0 and x > √32\frac{3}{2}

Calculations :

Let us take x2 = a, then

⇒ 4a2 - 37a + 9 = 0

⇒ 4a2 - 36a - a + 9 = 0

⇒ 4a(a - 9) -1(a - 9) = 0

⇒ (4a - 1)(a - 9) = 0

⇒ a = 1/4 and 9

x2 = 1/4 is not valid as x > √32\frac{3}{2} and x2 > 3/2

x2 = 9 such that x = 3, -3

Put x = 3, we get

 ⇒ 8x3 -27x3\frac{27}{x^3} 

⇒ 8(3)3 - 27/(3)3

⇒ 8(27) - 27/27

⇒ 216 - 1

⇒ 215