ABC26GN1997 · Surds and Indices

Subject: General Aptitude · Chapter: Surds and Indices · Exam: · Marks: · Difficulty:

If x = 2 + 2 + 23 , 3 then the value of x3 – 6x2 + 6x is (R.R.B., 2008) QUANTITATIVE APTITUDE

(a)1

(b)2

(c)3

(d)None of these

Answer

Answer (as printed): B

Explanation

x = 2 + 2 3 + 2 3 ⇒ ( x – 2) = 2 3 + 2 3 3  2 1  23 + 23  ⇒ (x – 2)3 =   2 1  2 1 = 2 + 2 + 3.2 3 · 2 3  2 3 + 2 3  2 ⇒ (x – 2)3 = 6 + 6 (x – 2) = 6 + 6x – 12 ⇒ (x – 2)3 = 6x – 6 ⇒ x3 – 8 – 6x (x – 2) = 6x – 6 ⇒ x3 – 8 – 6x2 + 12x = 6x – 6 ⇒ x3 – 6x2 + 6x = 2. QUANTITATIVE APTITUDE 5 −5 3

Explanation as extracted from the printed page; notation may be imperfect.

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