Question
If a, b and c are integers such that a 2 +
b 2 + c 2 = 228, a + b + c = 26 and b = c, then find the value of a?Solution
We know, (a + b + c) 2 = a 2 + b 2 + c 2 + 2(ab + bc + ac)
Then, 26 2 = 228 + 2(ab + b 2 + 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
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