Lahenda (sqrt{6}-sqrt{2})^2-frac{sqrt{6}-sqrt{2}}{sqrt{6}+sqrt{2}}

$$( \sqrt { 6 } - \sqrt { 2 } ) ^ { 2 } - \frac { \sqrt { 6 } - \sqrt { 2 } } { \sqrt { 6 } + \sqrt { 2 } }$$

Arvuta

$$6-3\sqrt{3}\approx 0,803847577$$

Lahenduse etapid

Kasutage kaksliikme \left(\sqrt{6}-\sqrt{2}\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

\sqrt{6} ruut on 6.

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

Tegurda 6=2\times 3. Kirjutage \sqrt{2\times 3} toote juured, kui see ruut \sqrt{2}\sqrt{3}.

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

Korrutage \sqrt{2} ja \sqrt{2}, et leida 2.

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

Korrutage -2 ja 2, et leida -4.

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

\sqrt{2} ruut on 2.

$$6-4\sqrt{3}+2-\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}}$$

Liitke 6 ja 2, et leida 8.

$$8-4\sqrt{3}-\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}}$$

Ratsionaliseerige korrutades lugeja ja \sqrt{6}-\sqrt{2} nimetaja \frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}} nimetaja.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}{\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}$$

Mõelge valemile \left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right). Korrutustehte saab ruutude vaheks teisendada järgmise reegli abil: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}{\left(\sqrt{6}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

Tõstke \sqrt{6} ruutu. Tõstke \sqrt{2} ruutu.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}{6-2}$$

Lahutage 2 väärtusest 6, et leida 4.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)}{4}$$

Korrutage \sqrt{6}-\sqrt{2} ja \sqrt{6}-\sqrt{2}, et leida \left(\sqrt{6}-\sqrt{2}\right)^{2}.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}-\sqrt{2}\right)^{2}}{4}$$

Kasutage kaksliikme \left(\sqrt{6}-\sqrt{2}\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

$$8-4\sqrt{3}-\frac{\left(\sqrt{6}\right)^{2}-2\sqrt{6}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{4}$$

\sqrt{6} ruut on 6.

$$8-4\sqrt{3}-\frac{6-2\sqrt{6}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{4}$$

Tegurda 6=2\times 3. Kirjutage \sqrt{2\times 3} toote juured, kui see ruut \sqrt{2}\sqrt{3}.

$$8-4\sqrt{3}-\frac{6-2\sqrt{2}\sqrt{3}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{4}$$

Korrutage \sqrt{2} ja \sqrt{2}, et leida 2.

$$8-4\sqrt{3}-\frac{6-2\times 2\sqrt{3}+\left(\sqrt{2}\right)^{2}}{4}$$

Korrutage -2 ja 2, et leida -4.

$$8-4\sqrt{3}-\frac{6-4\sqrt{3}+\left(\sqrt{2}\right)^{2}}{4}$$

\sqrt{2} ruut on 2.

$$8-4\sqrt{3}-\frac{6-4\sqrt{3}+2}{4}$$

Liitke 6 ja 2, et leida 8.

$$8-4\sqrt{3}-\frac{8-4\sqrt{3}}{4}$$

Jagage 8-4\sqrt{3} iga liige 4-ga, et saada 2-\sqrt{3}.

$$8-4\sqrt{3}-\left(2-\sqrt{3}\right)$$

Avaldise "2-\sqrt{3}" vastandi leidmiseks tuleb leida iga liikme vastand.

$$8-4\sqrt{3}-2+\sqrt{3}$$

Lahutage 2 väärtusest 8, et leida 6.

$$6-4\sqrt{3}+\sqrt{3}$$

Kombineerige -4\sqrt{3} ja \sqrt{3}, et leida -3\sqrt{3}.

$$6-3\sqrt{3}$$

Lahuta teguriteks

$$3 {(2 - \sqrt{3})} = 0,803847577$$