Lahenda (sqrt{-1}+sqrt{-2}-sqrt{-3})(sqrt{-1}-sqrt{-2}+sqrt{-3})

$$( \sqrt { - 1 } + \sqrt { - 2 } - \sqrt { - 3 } ) ( \sqrt { - 1 } - \sqrt { - 2 } + \sqrt { - 3 } )$$

Arvuta (complex solution)

$$4-2\sqrt{6}\approx -0,898979486$$

Lahenduse etapid

Arvutage -1 ruutjuur, et saada i.

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

Tegurda -2=2\left(-1\right). Kirjutage \sqrt{2\left(-1\right)} toote juured, kui see ruut \sqrt{2}\sqrt{-1}. -1 ruutjuur on i.

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

Tegurda -3=3\left(-1\right). Kirjutage \sqrt{3\left(-1\right)} toote juured, kui see ruut \sqrt{3}\sqrt{-1}. -1 ruutjuur on i.

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

Korrutage -1 ja i, et leida -i.

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

Arvutage -1 ruutjuur, et saada i.

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

Tegurda -2=2\left(-1\right). Kirjutage \sqrt{2\left(-1\right)} toote juured, kui see ruut \sqrt{2}\sqrt{-1}. -1 ruutjuur on i.

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

Korrutage -1 ja i, et leida -i.

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

Tegurda -3=3\left(-1\right). Kirjutage \sqrt{3\left(-1\right)} toote juured, kui see ruut \sqrt{3}\sqrt{-1}. -1 ruutjuur on i.

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

Rakendage distributiivsusomadus, korrutades avaldise i+\sqrt{2}i-i\sqrt{3} iga liikme avaldise i-i\sqrt{2}+\sqrt{3}i iga liikmega.

$$-1+\sqrt{2}+i\sqrt{3}i+i\sqrt{2}i+\left(\sqrt{2}\right)^{2}-\sqrt{3}\sqrt{2}+\sqrt{3}-\sqrt{3}\sqrt{2}+\left(\sqrt{3}\right)^{2}$$

Korrutage i ja i, et leida -1.

$$-1+\sqrt{2}-\sqrt{3}+i\sqrt{2}i+\left(\sqrt{2}\right)^{2}-\sqrt{3}\sqrt{2}+\sqrt{3}-\sqrt{3}\sqrt{2}+\left(\sqrt{3}\right)^{2}$$

Korrutage i ja i, et leida -1.

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

Kombineerige \sqrt{2} ja -\sqrt{2}, et leida 0.

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

\sqrt{2} ruut on 2.

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

Liitke -1 ja 2, et leida 1.

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

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

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

Kombineerige -\sqrt{3} ja \sqrt{3}, et leida 0.

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

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

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

Kombineerige -\sqrt{6} ja -\sqrt{6}, et leida -2\sqrt{6}.

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

\sqrt{3} ruut on 3.

$$1-2\sqrt{6}+3$$

Liitke 1 ja 3, et leida 4.

$$4-2\sqrt{6}$$

Reaalosa (complex solution)

$$4-2\sqrt{6}$$

Arvuta

$$\text{Indeterminate}$$