2018 · Q4
If 2b = a + c and y² = xz, then what is x^{b-c} y^{c-a} z^{a-b} equal to?
Elementary MathematicsAlgebra
- A3
- B2
- C1
- D-1
Explanation
From y² = xz, write y^(c−a) = (xz)^((c−a)/2). The expression becomes x^(b−c+(c−a)/2) · z^(a−b+(c−a)/2) = x^((2b−a−c)/2) · z^((a+c−2b)/2). The condition 2b = a + c makes both exponents zero. Hence the value is x⁰·z⁰ = 1, option (C).