Question

(|3radical 2 - 2 radical 3| totul supra 4 - |4radical 2 - 3 radical 3| totul supra 6 + | radical 2 - 2 radical 3| totul supra 12) : ( radical3/2) la puterea a 3 a

Answer 1

Analizam fiecare modul:

$3\sqrt2-2\sqrt3\ \textgreater \ 0 \Longrightarrow |3\sqrt2-2\sqrt3| = 3\sqrt2-2\sqrt3$

$4\sqrt2-3\sqrt3 \ \textgreater \ 0 \Longrightarrow |4\sqrt2-3\sqrt3 | = 4\sqrt2-3\sqrt3$

$\sqrt2-2\sqrt3\ \textless \ 0 \Longrightarrow |\sqrt2-2\sqrt3|= 2\sqrt3 -\sqrt2$

Expresia data devine:

$(\dfrac{3\sqrt2-2\sqrt3}{4} - \dfrac{4\sqrt2-3\sqrt3}{6} + \dfrac{2\sqrt3-\sqrt2}{12}):(\dfrac{\sqrt3}{2})^3$

Aducem la acelasi numitor in prima paranteza, numitorul comun este 12.

Se amplifica prima fractie cu 3, iar a doua cu 2 si obtinem :

[tex]\left(\dfrac{9\sqrt2-6\sqrt3-8\sqrt2+6\sqrt3+2\sqrt3-\sqrt2}{12}\right) : \\\;\\ \dfrac{\sqrt3\cdot\sqrt3\cdot\sqrt3}{8} = \dfrac{2\sqrt3}{12}\cdot\dfrac{8}{3\sqrt3} \\\;\\ = \dfrac{4}{9}[/tex]