Question

What are possible values of x and y, if
$2 \sqrt[3]{3xy} = - 4 \sqrt[3]{18}$
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Answer 1

Answer:

• y = -48/x . . . . . infinite possibilities
• for integer solutions, see below

Step-by-step explanation:

The equation can be put into more conventional form:

  $2\sqrt[3]{3xy}=-4\sqrt[3]{18} \qquad\text{given}\\\\\sqrt[3]{3xy}=-2\sqrt[3]{18} \qquad\text{divide by 2}\\\\3xy=-8\cdot 18 \qquad\text{cube both sides}\\\\y=\dfrac{-48}{x} \qquad\text{divide by 3x }$

This shows an inverse relationship between x and y. No specific values are indicated. There are an infinite number of possible pairs of values for x and y.

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Possible integer values are ...

  (x, y) ∈ {(-1, 48), (-2, 24), (-3, 16), (-4, 12), (-6, 8), (-8, 6), (-12, 4), (-16, 3), (-24, 2), (-48, 1), (1, -48), (2, -24), (3, -16), (4, -12), (6, -8), (8, -6), (12, -4), (16, -3), (24, -2), (48, -1)}