Question

упростите выражение.​

Answer 1

$( \sqrt{3} + 2) {}^{2} + 2 \sqrt{ 37 - 20 \sqrt{3} } = \\ = 3 + 4 \sqrt{3} + 4 + 2 \sqrt{5 {}^{2} - 2 \times 5 \times 2 \sqrt{3} + (2 \sqrt{3}) {}^{2} } = \\ = 7+ 4 \sqrt{3} + 2 \sqrt{(5 - 2 \sqrt{3} ) {}^{2} } = 7 + 4 \sqrt{3} + 2(5 - 2 \sqrt{3} ) = \\ = 7 + 4 \sqrt{3} + 10 - 4 \sqrt{3} = 17$