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SSC Selection Post 2020 PYQ — Question 54

SSC Selection Post - Matriculation Level - 9 Nov 2020 - Shift 3 • Quantitative Aptitude • Q54

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If x + y + z = 0, then (x + y + x )3 + (y + z - x)3 + (z + x - y)3 = k(xyz), where k is equal to:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. -3.

 

(x+y+x)3+(y+z−x)3+(z+x−y)3=k⋅xyz(x + y + x)^3 + (y + z - x)^3 + (z + x - y)^3 = k \cdot xyz

  1. x + y + x = 2x + y

  2. y + z - x

  3. z + x - y

(2x+y)3+(y+z−x)3+(z+x−y)3(2x + y)^3 + (y + z - x)^3 + (z + x - y)^3

If  x + y + z = 0, then:

(2x+y)3+(y+z−x)3+(z+x−y)3=−3xyz(2x + y)^3 + (y + z - x)^3 + (z + x - y)^3 = {-3xyz}

K = -3