Question

va rog frumos sa ma ajutați​

Answer 1

Răspuns:

a) 1

b) 4

c) 0

Explicație pas cu pas:

a)

$\frac{1}{ \sqrt{2 } + 1} + \frac{1}{ \sqrt{3} + \sqrt{2} } + \frac{1}{ \sqrt{4} + \sqrt{3} } = \sqrt{2} - 1 + \sqrt{3} - \sqrt{2} + 2 - \sqrt{3} = ( - 1) + \sqrt{3} + 2 - \sqrt{3 } = ( - 1) + 2 = 1$

b)

$\frac{1}{ \sqrt{2} + 1 } + \frac{3}{ \sqrt{5} + \sqrt{2} } + \frac{5}{ \sqrt{10} + \sqrt{5} } + \frac{15}{ \sqrt{25} + \sqrt{10} } = \sqrt{2} - 1 + \sqrt{5} - \sqrt{2} + \sqrt{10} - \sqrt{5} + \frac{15}{5 + \sqrt{10} } = \sqrt{2} - 1 + \sqrt{5} - \sqrt{2} + \sqrt{10} - \sqrt{5} + 5 - \sqrt{10} = ( - 1) + 5 = 4$

c)

$( \frac{2 \sqrt{3} }{2 \sqrt{3 + 3} } - \frac{6}{3 \sqrt{3 + 5} } ) \div ( \frac{1}{3 - 2 \sqrt{3} } - \frac{ \sqrt{3} }{3} ) = ( \frac{ \sqrt{3} }{ \sqrt{3 + 3} } - \frac{2}{ \sqrt{3 + 5} } ) \div ( \frac{1}{3 - 2 \sqrt{3} } - \frac{ \sqrt{3} }{3} ) = ( \frac{ \sqrt{3} }{ \sqrt{6} } - \frac{2}{ \sqrt{8} } ) \div ( \frac{1}{3 - 2 \sqrt{3} } - \frac{ \sqrt{3} }{3} ) = ( \frac{1}{ \sqrt{2} } - \frac{2}{2 \sqrt{2} } ) \div ( \frac{1}{3 - 2 \sqrt{3} } - \frac{ \sqrt{3} }{3} ) = ( \frac{1}{ \sqrt{2} } - \frac{1}{ \sqrt{2} } ) \div ( \frac{1}{3 - 2 \sqrt{3} } - \frac{ \sqrt{3} }{3} ) = 0 \div ( \frac{1}{3 - 2 \sqrt{3} } - \frac{ \sqrt{3} }{3} ) = 0$

sper ca te am ajutat!