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If | a − b − c 2a 2a | | 2b b − c − a 2b | = (a + b + c)(x + a + b + c)², x ≠ 0 and a + b + c ≠ 0, then x is equal to: | 2c 2c c − a − b |

1. −2(a + b + c)
2. 2(a + b + c)
3. abc
4. −(a + b + c)

Correct answer: −2(a + b + c)

Solution

Adding all rows factors out (a+b+c); reducing gives the determinant = (a+b+c)^3 = (a+b+c)(x+a+b+c)^2. So (x+a+b+c)^2 = (a+b+c)^2; since x != 0, x+a+b+c = -(a+b+c), giving x = -2(a+b+c).

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