Question
Quantitative Aptitude Question on Algebra
If a + b + c = 4, (a + b)2 + (b + c)2 + (c + a)2 = 20. Find the value of (a2 + b2 + c2).
A
4
B
8
C
6
D
2
Answer
4
Explanation
Solution
a+b+c=4 {given}
Squaring both sides, we get
(a + b + c)2 = 42
Or, a2 + b2 + c2 + 2ab + 2bc + 2ca = 16 … (I)
(a + b)2 + (b + c)2 + (c + a)2 = 20 {given}
Or, {a2 + b2 + 2ab} + {b2 + c2 + 2bc} + {a2 + c2 + 2ca} = 20
Or, 2(a2 + b2 + c2) + 2ab + 2bc + 2ca = 20
Or, 2(a2 + b2 + c2) + 16 - a2 - b2 - c2 = 20 [using equation (I)]
Or, (a2 + b2 + c2) + 16 = 20
Or, (a2 + b2 + c2) = 4
So, the correct option is (A) : 4.