Matematică, întrebare adresată de madalinapetrea17525, 8 ani în urmă

va rog e urgent am nevoie cine stie sa rezolve​

Anexe:

Răspunsuri la întrebare

Răspuns de Triunghiul1
16

\frac{1}{\sqrt{2} } +\frac{2}{\sqrt{8} } +\frac{3}{\sqrt{18} } =\frac{1}{\sqrt{2} } +\frac{2}{2\sqrt{2} } ^{(2}+\frac{3}{3\sqrt{2} } ^{(3}=\frac{1}{\sqrt{2} } +\frac{1}{\sqrt{2} } +\frac{1}{\sqrt{2} } =\frac{3}{\sqrt{2} } |\cdot \sqrt{2} =\frac{3\sqrt{2} }{2}

\frac{6}{\sqrt{3} } -\frac{8}{\sqrt{12} } +\frac{9}{\sqrt{27} } =\frac{6}{\sqrt{3} } -\frac{8}{2\sqrt{3} } ^{(2}+\frac{9}{3\sqrt{3} } ^{(3}=\frac{6}{\sqrt{3} } -\frac{4}{\sqrt{3} } +\frac{3}{\sqrt{3} }=\frac{5}{\sqrt{3}} |\cdot \sqrt{3} =\frac{5\sqrt{3} }{3}

(\frac{1}{\sqrt{5} } -\frac{1}{\sqrt{20} } +\frac{1}{\sqrt{45} } -\frac{1}{\sqrt{125} } )\cdot (2-\frac{1}{38} )=

(^{30)}\frac{1}{\sqrt{5} } -^{15)}\frac{1}{2\sqrt{5} } +^{10)}\frac{1}{3\sqrt{5} } -^{6)}\frac{1}{5\sqrt{5} } )\cdot (\frac{76}{38} -\frac{1}{38} )=

(\frac{30}{30\sqrt{5} } -\frac{15}{30\sqrt{5} } +\frac{10}{30\sqrt{5} } -\frac{6}{30\sqrt{5} } )\cdot \frac{75}{38} =

\frac{30-15+10-6}{30\sqrt{5} } \cdot \frac{75}{38} =\frac{19}{30\sqrt{5} } \cdot \frac{75}{38} =\frac{1}{2\sqrt{5} } \cdot \frac{5}{2} =\frac{5}{4\sqrt{5} } |\cdot \sqrt{5} =\frac{\sqrt{5} }{4}

(\sqrt{54} -^{\sqrt{6})} \frac{6}{\sqrt{6} } )\cdot (\frac{48}{\sqrt{6} } -\frac{15}{\sqrt{24} } )=(3\sqrt{6} -\frac{6\sqrt{6} }{6} ^{(6})\cdot (^{2)}\frac{48}{\sqrt{6} } -\frac{15}{2\sqrt{6} })=

=(3\sqrt{6} -\sqrt{6} )\cdot (\frac{96}{2\sqrt{6}}-\frac{15}{2\sqrt{6} } )=2\sqrt{6} \cdot \frac{81}{2\sqrt{6} } =81

Răspuns de dariusbarbu
10

Răspuns:

  •  \frac{3 \sqrt{2} }{2}
  •  \frac{5 \sqrt{3} }{3}
  • √5/4
  • 81

Explicație pas cu pas:

a) \:  \frac{1}{ \sqrt{2} }  +  \frac{2}{ \sqrt{8} }  +  \frac{3}{ \sqrt{18} }  =

 \frac{ \sqrt{2} }{2} +  \frac{2}{ 2\sqrt{2} }  +  \frac{3}{3 \sqrt{2} }  =

 \frac{ \sqrt{2} }{2}  +  \frac{1}{ \sqrt{2} }  +  \frac{1}{ \sqrt{2} } =

 \frac{ \sqrt{2} }{2}  +  \frac{ \sqrt{2} }{2}  +  \frac{ \sqrt{2} }{2}  =

 \frac{ \sqrt{2}  +  \sqrt{2}  +  \sqrt{2} }{2}  =

 \frac{3 \sqrt{2} }{2}

b) \:  \frac{6}{ \sqrt{3} }  -  \frac{8}{ \sqrt{12} }  +  \frac{9}{ \sqrt{27} }  =

2  \sqrt{3}  -  \frac{8}{2 \sqrt{3} } +  \frac{9}{3 \sqrt{3} }   =

2 \sqrt{3}  -  \frac{4}{ \sqrt{3} }  +  \frac{3}{ \sqrt{3} }  =

2 \sqrt{3}  -  \frac{4 \sqrt{3} }{3}  +  \sqrt{3}  =

 \frac{5 \sqrt{3} }{3}

c) \: ( \frac{1}{ \sqrt{5} }  -  \frac{1}{ \sqrt{20} }  +  \frac{1}{ \sqrt{45} }  -  \frac{1}{ \sqrt{125} } ) \times (2 -  \frac{1}{38} ) =

( \frac{1}{ \sqrt{5} }  -  \frac{1}{2 \sqrt{5} }  +  \frac{1}{3 \sqrt{5} }  -  \frac{1}{5 \sqrt{5} } ) \times  \frac{75}{38}  =

 \frac{19}{30 \sqrt{5} }  \times  \frac{75}{38}  =

 \frac{1}{2 \sqrt{5} }  \times  \frac{5}{2}  =

 \frac{5}{4 \sqrt{5} }  =

 \frac{ \sqrt{5} }{4}

d) \: ( \sqrt{54}  -  \frac{6}{ \sqrt{6} } ) \times ( \frac{48}{ \sqrt{6} }  -  \frac{15}{ \sqrt{24} }) =

(3 \sqrt{6}  -  \sqrt{6} ) \times ( \frac{48}{ \sqrt{6} }  -  \frac{15}{2 \sqrt{6} } ) =

2 \sqrt{6}  \times  \frac{81}{2 \sqrt{6} }  =

81

Alte întrebări interesante