Race against time!

Algebra Level 4

Suppose a,b,ca,b,c are real numbers that are in an arithmetic progression (in that order) such that a>b>ca>b>c.

And a2{a}^{2}, b2{b}^{2} and c2{c}^{2} are in a geometric progression (in that order) .

If a+b+c=32a+b+c=\frac { 3 }{ 2 } , what is the value of aa?

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