NandishSS wrote:Which of the following equations has only one integer pair as solution?
A) y = 2x
B) y = x/2
C) y=x √5
D) y=x+1
E) y=1/x
OA: C
The question wants us to pick an option that renders only one integer value of x and only one compatible integer value of y.
Let's discuss all the options one by one.
A) y = 2x => It implies that y is a multiple of '2;' thus, there can be many compatible integer values of x and y. For example, (x, y): (0, 0); (1, 2); (-1, -2), etc.
B) y = x/2 => x = 2y => It implies that x is a multiple of '2;' thus, there can be many compatible integer values of x and y. For example, (x, y): (0, 0); (2, 1); (-2, -1), etc.
C) y = x √5 => One of the integer pairs for (x, y) is (0, 0). To get y an integer value, x must be a multiple of √5; however, this will not serve the purpose as we want integer pairs for (x, y). Thus, y = x √5 has only one integer pairs for (x, y) i.e. (0, 0).
D) y = x+1 => Many integer pairs of values for x and y are possible. For example, (x, y): (0, 1); (-1, 0); (1, 2), etc.
E) y = 1/x => xy = 1 => If the product of two integers is '1,' they each can be either 1 or -1. Thus, there are two integer pairs for the values of x and y, and they are (1, 1) ans (-1, -1).
The correct answer:
C
Hope this helps!
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