Question

efectuati calculele : a) 12/v3+15/5v3-217v3+18/v3

b)8/3v2-8/2v2+8/6v2-8/12v2

c)24/5v6-12/v6+21/10v6-28/2v6

d)7/2v5+7/3v5-7/6v5+7/5v5



/ = supra
v = radical

cat mai repede​

Answer 1

Răspuns:

Explicație pas cu pas:

a) $\frac{12}{\sqrt{3}} + \frac{15}{5\sqrt{3}} - 217\sqrt{3} + \frac{18}{\sqrt{3} }$

    Rationalizam fractiile

    $\frac{12\sqrt{3} }{\sqrt{3}*\sqrt{3}} + \frac{15\sqrt{3} }{5\sqrt{3}*\sqrt{3}} - 217\sqrt{3} + \frac{18\sqrt{3} }{\sqrt{3}*\sqrt{3}}$

    $\frac{12\sqrt{3} }{3} + \frac{15\sqrt{3} }{5*3} - 217\sqrt{3} + \frac{18\sqrt{3} }{3} =$

    $\frac{12\sqrt{3} }{3} + \frac{15\sqrt{3} }{15} - 217\sqrt{3} + \frac{18\sqrt{3} }{3} =$

    Aducem la acelasi numitor comun (15)

    $\frac{12*5\sqrt{3} }{3*5} + \frac{15\sqrt{3} }{15} - \frac{217*15\sqrt{3}}{15} + \frac{18*5\sqrt{3} }{3*5}$

    $\frac{60\sqrt{3} }{15} + \frac{15\sqrt{3} }{15} - \frac{3255\sqrt{3}}{15} + \frac{90\sqrt{3} }{15} =$

    $\frac{60\sqrt{3} + 15\sqrt{3} - 3255\sqrt{3} + 90\sqrt{3}}{15}=$

    $\frac{165\sqrt{3} - 3255\sqrt{3}}{15}$

    $\frac{-3090\sqrt{3}}{15}$

    Simplificam prin 15

    $\frac{-206\sqrt{3}}{1} = -206\sqrt{3}$

b)  $\frac{8}{3\sqrt{2}} - \frac{8}{2\sqrt{2}} + \frac{8}{6\sqrt{2}} - \frac{8}{12\sqrt{2} }$

    Rationalizam fractiile

    $\frac{8\sqrt{2} }{3\sqrt{2}*\sqrt{2}} - \frac{8\sqrt{2} }{2\sqrt{2}*\sqrt{2}} + \frac{8\sqrt{2} }{6\sqrt{2}*\sqrt{2}} - \frac{8\sqrt{2} }{12\sqrt{2} *\sqrt{2}}$

    $\frac{8\sqrt{2} }{3*2} - \frac{8\sqrt{2} }{2*2} + \frac{8\sqrt{2} }{6*2} - \frac{8\sqrt{2} }{12*2}$

    $\frac{8\sqrt{2} }{6} - \frac{8\sqrt{2} }{4} + \frac{8\sqrt{2} }{12} - \frac{8\sqrt{2} }{24}$

    Aducem la acelasi numitor comun (24)

    $\frac{8*4\sqrt{2} }{6*4} - \frac{8*6\sqrt{2} }{4*6} + \frac{8*2\sqrt{2} }{12*2} - \frac{8\sqrt{2} }{24}$

    $\frac{32\sqrt{2} }{24} - \frac{48\sqrt{2} }{24} + \frac{16\sqrt{2} }{24} - \frac{8\sqrt{2} }{24}$

    $\frac{32\sqrt{2}- 48\sqrt{2} + 16\sqrt{2} - 8\sqrt{2}}{24}$

    $\frac{- 8\sqrt{2}}{24}$

    Simplificam prin 8

    $\frac{- 1\sqrt{2}}{4}$

Urmatoarele doua se rezolva similar cu primele.