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SSC CGL 2016 PYQ — Question 27

SSC CGL Tier II Quant - 30/11/2016 • Quantitative Aptitude • Q27

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If x = 1 + √2 + √3 , then find the value of 2x4 - 8x3 _ 8x2 + 32x.

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 16

x = 1 + √2 + √3

x - 1 = √2 + √3

Squaring both sides,

x2 - 2x + 1 = 5 + 2√6

x2 - 2x - 4 = 2√6 .....(1)

Squaring both sides,

x4 + 4x2 + 16 - 4x3 + 16x - 8x2 = 24

x4 - 4x3 _ 4x2 + 16x = 8

2x4 - 8x3 _ 8x2 + 32x = 16