Let a,b,c be real numbers and x,y,z be positive real numbers. If 2b = a + c and y² = xz, what is \(x^{b-c}y^{c-a}z^{a-b}\) equal to?
1
Write b = a + d and c = a + 2d. The expression becomes \(x^{-d}y^{2d}z^{-d}=(y^2/(xz))^d=1\). Thus the answer is 1.
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