[tex](7 - 4 \sqrt{3} )(2 + \sqrt{3} ) {}^{2} = (7 - 4 \sqrt{3} )(4 + 4 \sqrt{3} + 3) = 7 {}^{2} - (4 \sqrt{3} ) {}^{2} = 49 - 48 = 1[/tex]