Atrisiniet frac{sqrt{2}-2sqrt{3}}{sqrt{2}+2sqrt{3}}*frac{3sqrt{2}-2sqrt{3}}{3sqrt{2}-2sqrt{3}}

$$\frac { \sqrt { 2 } - 2 \sqrt { 3 } } { \sqrt { 2 } + 2 \sqrt { 3 } } \cdot \frac { 3 \sqrt { 2 } - 2 \sqrt { 3 } } { 3 \sqrt { 2 } - 2 \sqrt { 3 } }$$

Izrēķināt

$$\frac{2\sqrt{6}-7}{5}\approx -0,420204103$$

Atrisinājuma darbības

Daliet 3\sqrt{2}-2\sqrt{3} ar 3\sqrt{2}-2\sqrt{3}, lai iegūtu 1.

$$\frac{\sqrt{2}-2\sqrt{3}}{\sqrt{2}+2\sqrt{3}}\times 1$$

Atbrīvojieties no iracionalitātes saucēju ar \frac{\sqrt{2}-2\sqrt{3}}{\sqrt{2}+2\sqrt{3}}, reizinot skaitītāju un saucēju ar \sqrt{2}-2\sqrt{3}.

$$\frac{\left(\sqrt{2}-2\sqrt{3}\right)\left(\sqrt{2}-2\sqrt{3}\right)}{\left(\sqrt{2}+2\sqrt{3}\right)\left(\sqrt{2}-2\sqrt{3}\right)}\times 1$$

Apsveriet \left(\sqrt{2}+2\sqrt{3}\right)\left(\sqrt{2}-2\sqrt{3}\right). Reizināšanu var pārvērst par kvadrātu starpību, izmantojot šo kārtulu: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(\sqrt{2}-2\sqrt{3}\right)\left(\sqrt{2}-2\sqrt{3}\right)}{\left(\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}\times 1$$

Reiziniet \sqrt{2}-2\sqrt{3} un \sqrt{2}-2\sqrt{3}, lai iegūtu \left(\sqrt{2}-2\sqrt{3}\right)^{2}.

$$\frac{\left(\sqrt{2}-2\sqrt{3}\right)^{2}}{\left(\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}\times 1$$

Lietojiet Ņūtona binomu \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, lai izvērstu \left(\sqrt{2}-2\sqrt{3}\right)^{2}.

$$\frac{\left(\sqrt{2}\right)^{2}-4\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}}{\left(\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}\times 1$$

Skaitļa \sqrt{2} kvadrāts ir 2.

$$\frac{2-4\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}}{\left(\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}\times 1$$

Lai reiziniet \sqrt{2} un \sqrt{3}, reiziniet numurus zem kvadrātveida saknes.

$$\frac{2-4\sqrt{6}+4\left(\sqrt{3}\right)^{2}}{\left(\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}\times 1$$

Skaitļa \sqrt{3} kvadrāts ir 3.

$$\frac{2-4\sqrt{6}+4\times 3}{\left(\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}\times 1$$

Reiziniet 4 un 3, lai iegūtu 12.

$$\frac{2-4\sqrt{6}+12}{\left(\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}\times 1$$

Saskaitiet 2 un 12, lai iegūtu 14.

$$\frac{14-4\sqrt{6}}{\left(\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}\times 1$$

Skaitļa \sqrt{2} kvadrāts ir 2.

$$\frac{14-4\sqrt{6}}{2-\left(2\sqrt{3}\right)^{2}}\times 1$$

Paplašiniet \left(2\sqrt{3}\right)^{2}.

$$\frac{14-4\sqrt{6}}{2-2^{2}\left(\sqrt{3}\right)^{2}}\times 1$$

Aprēķiniet 2 pakāpē 2 un iegūstiet 4.

$$\frac{14-4\sqrt{6}}{2-4\left(\sqrt{3}\right)^{2}}\times 1$$

Skaitļa \sqrt{3} kvadrāts ir 3.

$$\frac{14-4\sqrt{6}}{2-4\times 3}\times 1$$

Reiziniet 4 un 3, lai iegūtu 12.

$$\frac{14-4\sqrt{6}}{2-12}\times 1$$

Atņemiet 12 no 2, lai iegūtu -10.

$$\frac{14-4\sqrt{6}}{-10}\times 1$$

Izsakiet \frac{14-4\sqrt{6}}{-10}\times 1 kā vienu daļskaitli.

$$\frac{14-4\sqrt{6}}{-10}$$

Sadalīt reizinātājos

$$\frac{2 \sqrt{6} - 7}{5} = -0,4202041028867288$$