Kangaroo solves the equation ax squared plus bx plus c equals 0, and beaver solves the equation bx squared plus ax plus c equals 0, where a, b, c are pairwise distinct non-zero integers. It turns out that the equations share a solution. Which of the following must be true? Let's let r be the common solution. Then, we know that ar squared plus br plus c equals br squared plus ar plus c. This will imply the following, and working through the algebra, we find that a minus b times r minus 1 times r equals 0. We know that c is not 0, and therefore we cannot have r equals 0. We also know a is not equal to b, and thus a minus b cannot be 0, and therefore we must have r equals 1. Since this is a solution, we can substitute it into the first equation, and we obtain a plus b plus c equals 0, and thus that's our correct answer.

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distinct integers

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a plus b plus c equals 0