Question

Answer 1

\(d,\left(1+\sqrt{3}-\sqrt{2}\right).\left(1+\sqrt{3}+\sqrt{2}\right)\)

\(=\left(1+\sqrt{3}\right)^2-2\)

\(=1+2\sqrt{3}+3-2\)

\(=2+2\sqrt{3}\)

Answer 2

`(1+\sqrt{3}-\sqrt{2}).(1+\sqrt{3}+\sqrt{2})`

`=[(1+\sqrt{3})-\sqrt{2}].[(1+\sqrt{3})+\sqrt{2}]`

`=(1+\sqrt{3})^2-(\sqrt{2})^2`

`=1+2\sqrt{3}+3-2=2+2\sqrt{3}`