Question

urgent va rog dau 100 de puncte si coroana

Answer 1

Răspuns:

cu creionul explicațiile, cu rosu formulele aplicate pe ex, cu albastru exercițiu propriu-zis.

sper sa te ajute. succes

Answer 2

Explicație pas cu pas:

a)

$2 - \sqrt{3} = \sqrt{4} - \sqrt{3} > 0 \implies |2 - \sqrt{3} | = 2 - \sqrt{3} \\ 1 - \sqrt{3} = \sqrt{1} - \sqrt{3} < 0 \implies |1 - \sqrt{3} | = \sqrt{3} - 1$

$|2 - \sqrt{3} | + |1 - \sqrt{3} | = 2 - \sqrt{3} - \sqrt{3} - 1 = 1$

b)

$1 - \sqrt{2} = \sqrt{1} - \sqrt{2} < 0 \implies |1 - \sqrt{2} | = \sqrt{2} - 1 \\ \sqrt{3} - 1 = \sqrt{3} - \sqrt{1} > 0 \implies |\sqrt{3} - 1| = \sqrt{3} - 1$

$\sqrt{8} - \sqrt{3} + \sqrt{ {(1 - \sqrt{2})}^{2} } + \sqrt{ {(\sqrt{3} - 1)}^{2} } = \sqrt{8} - \sqrt{3} + |1 - \sqrt{2}| + | \sqrt{3} - 1| = 2 \sqrt{2} - \sqrt{3} + \sqrt{2} - 1 + \sqrt{3} - 1 = 3 \sqrt{2} - 2$

c)

$2 - \sqrt{5} = \sqrt{4} - \sqrt{5} < 0 \implies |2 - \sqrt{5} | = \sqrt{5} - 2 \\ \sqrt{3} - 2 = \sqrt{3} - \sqrt{4} < 0 \implies |\sqrt{3} - 2 | = 2 - \sqrt{3}$

$|2 - \sqrt{5} | + | \sqrt{5} + \sqrt{3} | + |\sqrt{3} - 2 | = \sqrt{5} - 2 + \sqrt{5} + \sqrt{3} + 2 - \sqrt{3} = 2 \sqrt{5}$

d)

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

$\sqrt{ {( \sqrt{2} + 3)}^{2} } + \sqrt{ {( \sqrt{2} - 3)}^{2} } = |\sqrt{2} + 3| + |\sqrt{2} - 3| = \sqrt{2} + 3 + 3 - \sqrt{2} = 6$

e)

$2 \sqrt{3} - \sqrt{18} + 2 \sqrt{ {( \sqrt{3} - 2)}^{2} } + 3 \sqrt{ {( \sqrt{2} - 1)}^{2} } = 2 \sqrt{3} - 3 \sqrt{2} + 2 | \sqrt{3} - 2| + 3 | \sqrt{2} - 1| = 2 \sqrt{3} - 3 \sqrt{2} + 2(2 - \sqrt{3}) + 3(\sqrt{2} - 1) = 2 \sqrt{3} - 3 \sqrt{2} + 4 - 2\sqrt{3} + 3\sqrt{2} - 3 = 1$