Question

If (x+y)^2 =42 and (x^2+y^2)=12, find the value of 2xy

Answer 1

Using the binomial square identity and the two given equations (x+y)^2 = 42 and x^2 + y^2 = 12, we found that the value of 2xy is 30. Therefore, the value of 2xy is 30.

Step-by-step explanation:

To solve the given problem, we recall the identity for the square of a binomial: (x+y)^2 = x^2 + 2xy + y^2. Given that (x+y)^2 = 42 and x^2 + y^2 = 12, we can substitute the latter into the former to find the value of 2xy.

We start with the equation (x+y)^2 = 42:

• x^2 + 2xy + y^2 = 42

We are also given that x^2 + y^2 = 12, so we plug this into the equation above:

• 12 + 2xy = 42

Subtracting 12 from both sides, we get:

• 2xy = 42 - 12
• 2xy = 30

Therefore, the value of 2xy is 30.