Question
Quantitative Aptitude Question on Algebra
If a, b and c are integers such that a2 + b2 + c2 = 228, a + b + c = 26 and b = c, then what is the value of a ?
A
8
B
10
C
12
D
6
E
14
Answer
10
Explanation
Solution
We know, (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ac)
Then, 262 = 228 + 2(ab + b2 + ab)
224 = b(2a + b)
And, a + b + b = 26
a = 26 - 2b
Now, 224 = b(2(26 - 2b) + b)
b = 8, 28/3 (but b is an integer)
Then, b = 8 = c
Therefore, a = 26 - 2 * 8 = 10
So, the correct option is (B) : 10.