Question:
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 ?
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 ?
Updated On: Apr 28, 2025
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The Correct Option is B
Solution and Explanation
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.
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.
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