If z=∛x, then z is the cube root of x, and x=z3. z3 is another way of writing z×z×z, that is, z multiplied by itself three times.
Example: If x=64=4×4×4, then z=4, making 4 the cube root of 64.
The equation x2+(y-∛x2)2=1 can also be written x2+(y-x⅔)2=1.
This can be expanded: x2+y2-2x⅔y+x4/3=1, but since there are two variables x and y and only one equation, this is a relationship and there are an infinite number of solutions (i.e., values of x and y) satisfying the relation. The equation can be used for drawing a graph. The graph is a cardioid (heart shape):
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