Child Labor #7
Algebra
Level
4
Choose the correct option satisfying the above system of equations.
a, b, c are in A.P.
a, c, b are in A.P.
b, a , c are in A.P.
None of the other choices.
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1 solution
Three cyclic equations with unequal values show that a, b, and c are mutually unequal. Multiplying first equation by (a - b) gives a 3 − b 3 = 2 ( a − b ) . Likewise b 3 − c 3 = b − c ; and c 3 − a 3 = 3 ( c − a ) . Adding all the three, 0 = 2 a − 2 b + b − c + 3 c − 3 a → 2 c − a − b = 0 , → 2 c = a + b . Hence a, c, b are in A.P.