Lahenda (2sqrt{2}-1)^2-(1+sqrt{3})*(sqrt{2}-sqrt{6})

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

Arvuta

$$9-2\sqrt{2}\approx 6,171572875$$

Lahenduse etapid

Kasutage kaksliikme \left(2\sqrt{2}-1\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

\sqrt{2} ruut on 2.

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

Korrutage 4 ja 2, et leida 8.

$$8-4\sqrt{2}+1-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

Liitke 8 ja 1, et leida 9.

$$9-4\sqrt{2}-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

Kasutage distributiivsusomadust, et korrutada 1+\sqrt{3} ja \sqrt{2}-\sqrt{6}.

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{6}+\sqrt{3}\sqrt{2}-\sqrt{3}\sqrt{6}\right)$$

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

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{6}+\sqrt{6}-\sqrt{3}\sqrt{6}\right)$$

Kombineerige -\sqrt{6} ja \sqrt{6}, et leida 0.

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{3}\sqrt{6}\right)$$

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

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{3}\sqrt{3}\sqrt{2}\right)$$

Korrutage \sqrt{3} ja \sqrt{3}, et leida 3.

$$9-4\sqrt{2}-\left(\sqrt{2}-3\sqrt{2}\right)$$

Kombineerige \sqrt{2} ja -3\sqrt{2}, et leida -2\sqrt{2}.

$$9-4\sqrt{2}-\left(-2\sqrt{2}\right)$$

Arvu -2\sqrt{2} vastand on 2\sqrt{2}.

$$9-4\sqrt{2}+2\sqrt{2}$$

Kombineerige -4\sqrt{2} ja 2\sqrt{2}, et leida -2\sqrt{2}.

$$9-2\sqrt{2}$$