Question

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

• A. 2
• B. 1
• C. 0
• D. 1

Answer 1

The Correct Option is D

We are given the following two equations: \[ x + y = 2 \quad (1) \] \[ x^2 + y^2 = 2 \quad (2) \] To find \( xy \), we use the identity: \[ (x + y)^2 = x^2 + y^2 + 2xy \] Substitute the values from equations (1) and (2): \[ (2)^2 = 2 + 2xy \] \[ 4 = 2 + 2xy \] Simplify the equation to solve for \( xy \): \[ 4 - 2 = 2xy \quad \Rightarrow \quad 2 = 2xy \] \[ xy = 1 \] Use the identity \( (x + y)^2 = x^2 + y^2 + 2xy \) to relate the sum and squares of two variables to their product.