Let x > 0 and y > 0. Suppose that xy^2 = 6 and x^2*y^6 = 72xy. What is the value of xy? Express your answer in simplest radical form.
+128406 xy^2 = 6 → x = 6/y^2 (1)
x^2 y^6 = 72xy → xy^5 = 72 (2)
Sub (1) into (2)
(6/y^2) * y^5 = 72
6 * y^3 = 72
y^3 = 72/6 = 12
y = (12)^(1/3)
x= 6 / [ 12^(1/3) ] ^2 = 6 / (12)^(2/3)
xy = 6/ (12^(2/3) * 12^(1/3) = 6 / (12^(1/3) = [6 ] / [ 2^(1/3) * 6^(1/3) ] = (6)^(2/3) / (2^(1/3) =
3^(2/3) * 2^(2/3) / 2^(1/3) =
(9)^(1/3) * 2^(1/3) =
∛9 * ∛2 =
∛18
