SOLUTION: Let x and y be nonzero, real numbers such that -1 < x < 1 and -2 < y < 2. Suppose x/y + y/x = z, where z is some real number. Which of the following is true for all possible z? cho
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-> SOLUTION: Let x and y be nonzero, real numbers such that -1 < x < 1 and -2 < y < 2. Suppose x/y + y/x = z, where z is some real number. Which of the following is true for all possible z? cho
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Question 474645: Let x and y be nonzero, real numbers such that -1 < x < 1 and -2 < y < 2. Suppose x/y + y/x = z, where z is some real number. Which of the following is true for all possible z? choose the answer and explain the reason to choose your response
z is less than 10^k for some k>1
z is positive
xyz can be negative
The other three answers are false Answer by richard1234(7193) (Show Source):
The first choice "z is less than 10^k for some k>1" is not necessarily true (even if we let k get really large) because z can also go to infinity.
z does not have to be positive (e.g. let x and y have different signs).
xyz can be negative, but xyz can also be positive (let x,y be positive).
Hence, the last choice "the other three answers are false" is correct because the first three choices have counterexamples; i.e. the statements are not true for all possible z.
