Carcass wrote:
If \(x^2y^3<0\), which of the following must be true?
Indicate all such answers.
A. \(x>0\)
B. \(xy<0\)
C. \(x^2y<0\)
D. \(xy^2>0\)
E. \(x^2>0\)
F. \(y^2>0\)
G. \(xy≠0\)
Given \(x^2y^3<0\), so neither of them is = 0, so G is one of the choice.
since x is squared, sign of x does not matter and y is cubed and still < 0 so y has to be negative.
Among the choices,
A. \(x>0\) - sign of x does not matter - No
B. \(xy<0\) - sign of x does not matter - No
C. \(x^2y<0\) - y is negative - True
D. \(xy^2>0\) - sign of x does not matter - No
E. \(x^2>0\) - sign of x does not matter, so \(x^2\) is always positive - True
F. \(y^2>0\) - \(y^2\) is always positive - True
G. \(xy≠0\) - Neither can't be = 0 - True