Question

Calculati: b si c Va rog​

Answer 1

Explicație pas cu pas:

a)

$2 - \sqrt{5} = \sqrt{4} - \sqrt{5} < 0 \implies \\ |2 - \sqrt{5}| = - (2 - \sqrt{5}) = \sqrt{5} - 2$

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

$\sqrt{ {(2 - \sqrt{5} )}^{2}} + \sqrt{ {(3 - \sqrt{5} )}^{2}} = |2 - \sqrt{5}| + |3 - \sqrt{5}| = \sqrt{5} - 2 + 3 - \sqrt{5} = ( \sqrt{5} - \sqrt{5} ) + (3 - 2) = \bf 1$

b)

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

$\sqrt{7} - 2 = \sqrt{7} - \sqrt{4} > 0 \\ \implies |\sqrt{7} - 2| = \sqrt{7} - 2$

$\sqrt{ {(3 - \sqrt{7} )}^{2} } + \sqrt{ {(\sqrt{7} - 2)}^{2} } = 3 - \sqrt{7} + \sqrt{7} - 2 = \bf 1$

c)

$\sqrt{8} - 3 = \sqrt{8} - \sqrt{9} < 0 \implies \\ |\sqrt{8} - 3| = - (\sqrt{8} - 3) = 3 - \sqrt{8}$

$5 - \sqrt{18} = \sqrt{25} - \sqrt{18} > 0 \\ \implies |5 - \sqrt{18}| = 5 - \sqrt{18}$

$7 - \sqrt{50} = \sqrt{49} - \sqrt{50} < 0 \implies \\ |7 - \sqrt{50}| = - (7 - \sqrt{50}) = \sqrt{50} - 7$

$\sqrt{ {( \sqrt{8} - 3)}^{2} } + \sqrt{ {(5 - \sqrt{18} )}^{2} } + \sqrt{ {(7 - \sqrt{50} )}^{2} } = | \sqrt{8} - 3| + |5 - \sqrt{18} | + |7 - \sqrt{50} | = 3 - \sqrt{8} + 5 - \sqrt{18} + \sqrt{50} - 7 = (3 + 5 - 7) - 2 \sqrt{2} - 3 \sqrt{2} + 5 \sqrt{2} = 8 - 1 + 5 \sqrt{2} - 5 \sqrt{2} = \bf 1$