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For real numbers a, b, c (all non-zero), suppose a² + b² + c² = ab + bc + ca. If the value of (b+c)/a + (a+c)/b + (a+b)/c is denoted by lambda, find the value of lambda.

1. 2
2. 4
3. 6
4. 8

Correct answer: 6

Solution

The condition implies a = b = c (since each squared difference must be zero); substituting gives each term (b+c)/a = 2, so lambda = 2 + 2 + 2 = 6.

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