(2+V3) ^2+ (2-V3) ^2

To evaluate the expression \((2 + \sqrt{3})^2 + (2 - \sqrt{3})^2\), we can calculate each squared term separately and then add them together. 1. Calculate \((2 + \sqrt{3})^2\): \[ (2 + \sqrt{3})^2 = 2^2 + 2 \cdot 2 \cdot \sqrt{3} + (\sqrt{3})^2 = 4 + 4\sqrt{3} + 3 = 7 + 4\sqrt{3} \] 2. Calculate \((2 - \sqrt{3})^2\): \[ (2 - \sqrt{3})^2 = 2^2 - 2 \cdot 2 \cdot \sqrt{3} + (\sqrt{3})^2 = 4 - 4\sqrt{3} + 3 = 7 - 4\sqrt{3} \] 3. Now add the two results together: \[ (7 + 4\sqrt{3}) + (7 - 4\sqrt{3}) = 7 + 7 + 4\sqrt{3} - 4\sqrt{3} = 14 \] Thus, the result of \((2 + \sqrt{3})^2 + (2 - \sqrt{3})^2\) is \(\boxed{14}\).