If \(x + y = 2\) and \(x^2 + y^2 = 2,\) what is the value of \(xy ?\)

[Vincen]

If \(x + y = 2\) and \(x^2 + y^2 = 2,\) what is the value of \(xy ?\)

A. –2
B. –1
C. 0
D. 1
E. 2

[spoiler]OA=D[/spoiler]

Source: Official Guide

[Scott@TargetTestPrep]

If \(x + y = 2\) and \(x^2 + y^2 = 2,\) what is the value of \(xy ?\)

A. –2
B. –1
C. 0
D. 1
E. 2

[spoiler]OA=D[/spoiler]

Source: Official Guide

Squaring both sides of the first equation, we have:

(x + y)^2 = 2^2

x^2 + y^2 + 2xy = 4

Since we are given that x^2 + y^2 = 2, we have:

2 + 2xy = 4

2xy = 2

xy = 1

Answer: D