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SSC Selection Post 2022 PYQ — Question 68

SSC Selection Post - Matriculation Level 2022 - 14 March 2022 - Shift 1 • Quantitative Aptitude • Q68

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If 2x22x ^ 2 + 5x - 1 = 0 then what is the value of x3 x ^ 3 -1/(8x3) 1/(8x ^ 3)?

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. −1558-\frac{155}{8}.

(a - b)3 = a3 - b3 - 3ab(a - b)

2x2 + 5x - 1 = 0

(2x2/x) + (5x/2x) - (1/2x) = 0

⇒ x + (5/2) - (1/2x) = 0

⇒ x - (1/2x) = -5/2      ---- (1)

So, (-5/2)3 = (x3) - (1/2x)3 - 3 × x × (1/2x) (x - 1/2x)

⇒ -125/8 = x3 - (1/8x3) - (3/2) (-5/2) (From 1)

⇒ -125/8 = x3 - (1/8x3) + (15/4)

⇒ (-125/8) - (15/4) = x3 - (1/8x3)

⇒ (-125 - 30)/8 = x3 - (1/8x3)

⇒ -155/8 = x3 - (1/8x3)