Question

Answer 1

\(\left(2+\sqrt{3}\right)^2+\left(2-\sqrt{3}\right)^2\\ =2^2+2\cdot2\cdot\sqrt{3}+\left(\sqrt{3}\right)^2+2^2-2\cdot2\cdot\sqrt{3}+\left(\sqrt{3}\right)^2\\ =4+4\sqrt{3}+3+4-4\sqrt{3}+3\\ =8+6=14\)

Answer 2

\(\left(2+\sqrt[]{3}\right)^2+\left(2-\sqrt[]{3}\right)^2\)

\(=\left(2+\sqrt[]{3}+2-\sqrt[]{3}\right)^2-2\left(2+\sqrt[]{3}\right)\left(2-\sqrt[]{3}\right)\)

\(=16-2.\left(4-3\right)=14\)