Răspuns:
Explicație pas cu pas:
√8=2√2
√18=3√2
√72=6√2
1/2√2 +1/3√2 +1/6√2 =
√2/4 +√2/6 +√2/12 =
(3√2+2√2+√2) /12 =
6√2 /12=
=√2 /2
Răspuns:
[tex]\frac{\sqrt{2}}{2}[/tex]
Explicație pas cu pas:
Inversul unui numai a reprezinta [tex]\frac{1}{a}[/tex]
[tex]\frac{1}{a} + \frac{1}{b} + \frac{1}{c} =\\\\\frac{1}{\sqrt{8} } + \frac{1}{\sqrt{18} } = \frac{1}{\sqrt{72} } = \\\\[/tex]
Descompunem radicalii de la numitor:
[tex]\sqrt{8} = \sqrt{2^{3} = 2\sqrt{2} \\\\[/tex]
[tex]\sqrt{18} = \sqrt{3^{2}*2 = 3\sqrt{2} \\\\[/tex]
[tex]\sqrt{72} = \sqrt{3^{2}*2^{3} = 6\sqrt{2} \\\\[/tex]
[tex]\frac{1}{2\sqrt{2} } + \frac{1}{3\sqrt{2} } + \frac{1}{6\sqrt{2} } =[/tex]
Rationalizam fiecare fractie cu [tex]\sqrt{2}[/tex]
[tex]\frac{\sqrt{2}}{2*2} + \frac{\sqrt{2}}{3*2} + \frac{\sqrt{2}}{6*2} =[/tex][tex]\frac{\sqrt{2}}{4} + \frac{\sqrt{2}}{6} + \frac{\sqrt{2}}{12} =[/tex]
Aducem la acelasi numitor comun 12
[tex]\frac{3\sqrt{2} }{4*3} + \frac{2\sqrt{2} }{6*2} + \frac{\sqrt{2} }{12} = \\\\\frac{3\sqrt{2} }{12} + \frac{2\sqrt{2} }{12} + \frac{\sqrt{2} }{12} = \\\\\frac{3\sqrt{2}+2\sqrt{2}+\sqrt{2} }{12} = \\\\\frac{6\sqrt{2} }{12} = \\\\\frac{\sqrt{2} }{2} = \\[/tex]
