If `x+y=4` and `xy=2,` find the values of `x^2+y^2`

Explanation

To find the value of \( x^2 + y^2 \) given that \( x + y = 4 \) and \( xy = 2 \), we can follow these steps:

### Step 1: Use the identity for \( (x + y)^2 \)
We know that:
\[ (x + y)^2 = x^2 + 2xy + y^2 \]
Given \( x + y = 4 \), we can square both sides:
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