Question

Calculati suma inverselor numerelor a b c unde:
$a \sqrt{8}$
$b \sqrt{18}$
$c \sqrt{72}$
cu explicatie va rogg​

Answer 1

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

Answer 2

Răspuns:

$\frac{\sqrt{2}}{2}$

Explicație pas cu pas:

Inversul unui numai a reprezinta $\frac{1}{a}$

$\frac{1}{a} + \frac{1}{b} + \frac{1}{c} =\\\\\frac{1}{\sqrt{8} } + \frac{1}{\sqrt{18} } = \frac{1}{\sqrt{72} } =$

Descompunem radicalii de la numitor:

$\sqrt{8} = \sqrt{2^{3} = 2\sqrt{2}$

$\sqrt{18} = \sqrt{3^{2}*2 = 3\sqrt{2}$

$\sqrt{72} = \sqrt{3^{2}*2^{3} = 6\sqrt{2}$

$\frac{1}{2\sqrt{2} } + \frac{1}{3\sqrt{2} }  + \frac{1}{6\sqrt{2} } =$

Rationalizam fiecare fractie cu $\sqrt{2}$

$\frac{\sqrt{2}}{2*2} + \frac{\sqrt{2}}{3*2} + \frac{\sqrt{2}}{6*2} =$$\frac{\sqrt{2}}{4}  + \frac{\sqrt{2}}{6} + \frac{\sqrt{2}}{12} =$

Aducem la acelasi numitor comun 12

$\frac{3\sqrt{2} }{4*3}  + \frac{2\sqrt{2} }{6*2} + \frac{\sqrt{2} }{12} = \\\\\frac{3\sqrt{2} }{12}  + \frac{2\sqrt{2} }{12} + \frac{\sqrt{2} }{12} = \\\\\frac{3\sqrt{2}+2\sqrt{2}+\sqrt{2} }{12} = \\\\\frac{6\sqrt{2} }{12} = \\\\\frac{\sqrt{2} }{2} =$