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SSC CGL 2019 PYQ — Question 72

SSC CGL - 6th June 2019 - Shift 1 • Quantitative Aptitude • Q72

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If ab + bc + ca = 8 and a2 + b2 + c2 = 20, then a possible value of 1/2 × (a + b + c)[(a - b)2 + (b - c)2 + (c - a)2] is:

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Correct answer: A

Explanation

Correct Answer is option 1 i.e. 72

Concept

Understanding

Application

(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx

ab + bc + ca = 8 and 

a2 + b2 + c2 = 20

Using the formula:

(a + b + c)2 = 20 + 2 × 8 = 36

(a + b + c) = 6

Now,

1/2 (a + b + c) [(a – b) 2 + (b – c) 2 + (c – a)2] 

= 1/2 (a + b + c) [2(a2 + b2 + c2) – 2(ab + bc + ca)]

= 1/2 × 6 × [2 × (20 – 8)]

= 3 × 24

= 72