SOLUTION: z^1/2-4z^1/4+4=0

Question 338157: z^1/2-4z^1/4+4=0
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
z^1/2-4z^1/4+4=0

z^(1/2) - 4z^(1/4) + 4 = 0 (placed these fractional exponents in parenthesis)
z^(1/2) = (z^(1/4))^2 = z^(1/4 * 2) = z^(1/2) (you multiply exponents in this case)
(z^(1/4) - 2)(z^(1/4) - 2) = 0
z^(1/2) - 2 * z^(1/4) - 2 * z^(1/4) + 4 = 0 (used FOIL)
z^(1/2) - 4z^(1/4) + 4 = 0 (simplified)

z^(1/4) = 2 (this means the 4th root of z is 2)
(z^(1/4))^4 = 2^4 (take both sides to the 4th power)
z = 16

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