Question

8. Explicitează modulul: a) |√5-√7; b) 3-√7); c) |√5-3); 4) (2√/5-3√/7); e) 3√/3-2/7; 1) 1√5-9; g) 5√5-4√5). 9. Calculează: a) 1.4 2: b) - 17:4 3./21 3.24) 1 12+12 5.​

Answer 1

Explicație pas cu pas:

$\sqrt{5} - \sqrt{7} < 0 \implies | \sqrt{5} - \sqrt{7} | = \sqrt{7} - \sqrt{5}$

$3 - \sqrt{7} = \sqrt{9} - \sqrt{7} > 0 \\ \implies |3 - \sqrt{7}| = 3 - \sqrt{7}$

$\sqrt{5} - 3 = \sqrt{5} - \sqrt{9} < 0 \\ \implies | \sqrt{5} - 3| = 3 - \sqrt{5}$

$2 \sqrt{5} - 3 \sqrt{7} = \sqrt{20} - \sqrt{42} < 0 \\ \implies |2 \sqrt{5} - 3 \sqrt{7}| = 3 \sqrt{7} - 2 \sqrt{5}$

$3 \sqrt{3} - 2\sqrt{7} = \sqrt{27} - \sqrt{28} < 0 \\ \implies |3 \sqrt{3} - 2\sqrt{7}| = 2 \sqrt{7} - 3 \sqrt{3}$

$5 \sqrt{5} - 4\sqrt{5} > 0 \implies |5 \sqrt{5} - 4\sqrt{5}| = 5 \sqrt{5} - 4\sqrt{5}$