Question

A. (2√3-1)^2 - (√3-√2)(√3+√2)

Answer 1

\(A=\left(2\sqrt{3}-1\right)^2-\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)\\ =\left[\left(2\sqrt{3}\right)^2-2.2\sqrt{3}.1+1^2\right]-\left[\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2\right]\\ =\left[12-4\sqrt{3}+1\right]-\left[3-2\right]\\ =13-4\sqrt{3}-1=12-4\sqrt{3}\)

Answer 2

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

\(=12-4\sqrt[]{3}+1-\left(3-1\right)\)

\(=12-4\sqrt[]{3}+1-3+1\)

\(=11-4\sqrt[]{3}\)