Lahenda frac{2sqrt{3}-sqrt{2}}{2sqrt{3}+sqrt{2}}

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

Arvuta

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

Lahenduse etapid

Ratsionaliseerige korrutades lugeja ja 2\sqrt{3}-\sqrt{2} nimetaja \frac{2\sqrt{3}-\sqrt{2}}{2\sqrt{3}+\sqrt{2}} nimetaja.

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

Mõelge valemile \left(2\sqrt{3}+\sqrt{2}\right)\left(2\sqrt{3}-\sqrt{2}\right). Korrutustehte saab ruutude vaheks teisendada järgmise reegli abil: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Korrutage 2\sqrt{3}-\sqrt{2} ja 2\sqrt{3}-\sqrt{2}, et leida \left(2\sqrt{3}-\sqrt{2}\right)^{2}.

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

Kasutage kaksliikme \left(2\sqrt{3}-\sqrt{2}\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

\sqrt{3} ruut on 3.

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

Korrutage 4 ja 3, et leida 12.

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

\sqrt{3} ja \sqrt{2} korrutage numbrid, mis on sama juur.

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

\sqrt{2} ruut on 2.

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

Liitke 12 ja 2, et leida 14.

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

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

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

Arvutage 2 aste 2 ja leidke 4.

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

\sqrt{3} ruut on 3.

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

Korrutage 4 ja 3, et leida 12.

$$\frac{14-4\sqrt{6}}{12-\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} ruut on 2.

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

Lahutage 2 väärtusest 12, et leida 10.

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

Lahuta teguriteks

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