If x + y is rational, must x and y each be rational?

A) Yes; because the sum of rationals is rational.

B) No; because the sum of irrationals is always irrational.

C) No; because x and y could be additive inverses of each other.

D) Yes; because x and y must be integers, and integers are rational.

Question

Renee

8 May, 02:57

+2

Answers (1)

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Maryjane Bartlett · Answer 1

It depends because x could be pi and y could be - pi. Both are irrational though they add up to 0 which is rational so I dont know, either B or C

If x + y is rational, must x and y each be rational?A) Yes; because the sum of rationals is rational.B) No; because the sum of irrationals is always irrational.C) No; because x and y could be additive inverses of each other.D) Yes; because x and y must be integers, and integers are rational.