Question

5. Valoarea numărului:
√(1-√3)²-√(√3-2)²-√(3-2√3)²-√(5-3√3)²-3√(√3-3)=​

Answer 1

Explicație pas cu pas:

$1 - \sqrt{3} = \sqtex1} - \sqrt{3} < 0 \\ \implies |1 - \sqrt{3}| = \sqrt{3} - 1$

$\sqrt{3} - 2 = \sqrt{3} - \sqrte4} < 0 \\ \implies |\sqrt{3} - 2| = 2 - \sqrt{3}$

$3 - 2\sqrt{3} = \sqrt{9} - \sqrt{12} < 0 \\ \implies |3 - 2\sqrt{3}| = 2\sqrt{3} - 3$

$5 - 3\sqrt{3} = \sqrt{25} - \sqrt{27} < 0 \\ \implies |5 - 3\sqrt{3}| = 3\sqrt{3} - 5$

$\sqrt{3} - 3 = \sqrt{3} - \sqrt{9} < 0 \\ \implies |\sqrt{3} - 3| = 3 - \sqrt{3}$

$= |1 - \sqrt{3}| - |\sqrt{3} - 2| - |3 - 2\sqrt{3}| - |5 - 3\sqrt{3}| - 3|\sqrt{3} - 3| = </p><p>(\sqrt{3} - 1) - (2 - \sqrt{3}) - (2 \sqrt{3} - 3) - (3 \sqrt{3} - 5) - 3(3 - \sqrt{3}) = \sqrt{3} - 1 - 2 + \sqrt{3} - 2 \sqrt{3} + 3 - 3 \sqrt{3} + 5 - 9 + 3\sqrt{3} = (5 \sqrt{3} - 5 \sqrt{3}) + (8 - 12) = 0 - 4 = - 4 \bf$