Question:
If a, b, c, and d are integers such that \(a + b + c + d = 30\), then the minimum possible value of \((a - b)^2 + (a - c)^2 + (a - d)^2\) is
If a, b, c, and d are integers such that \(a + b + c + d = 30\), then the minimum possible value of \((a - b)^2 + (a - c)^2 + (a - d)^2\) is
Updated On: Sep 26, 2024
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The Correct Option is B
Solution and Explanation
The expression \(a+b+c+d=30\), where \(a,b,c,d \) are integers.
To maximize the value of \((a−b)^2+(a−c)^2+(a−d)^2\), each bracket should have the least possible value.
Choosing the values \((a,b,c,d)=(8,8,7,7),\) the given expression evaluates to 2, and it cannot have a smaller value.
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