Lahenda 19*(sqrt{5}-sqrt{3}+sqrt{2})(sqrt{5}-sqrt{3}-sqrt{2})

$$19 \cdot ( \sqrt { 5 } - \sqrt { 3 } + \sqrt { 2 } ) ( \sqrt { 5 } - \sqrt { 3 } - \sqrt { 2 } )$$

Arvuta

$$114-38\sqrt{15}\approx -33,173367156$$

Lahenduse etapid

Kasutage distributiivsusomadust, et korrutada 19 ja \sqrt{5}-\sqrt{3}+\sqrt{2}.

$$\left(19\sqrt{5}-19\sqrt{3}+19\sqrt{2}\right)\left(\sqrt{5}-\sqrt{3}-\sqrt{2}\right)$$

Rakendage distributiivsusomadus, korrutades avaldise 19\sqrt{5}-19\sqrt{3}+19\sqrt{2} iga liikme avaldise \sqrt{5}-\sqrt{3}-\sqrt{2} iga liikmega.

$$19\left(\sqrt{5}\right)^{2}-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{5} ruut on 5.

$$19\times 5-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Korrutage 19 ja 5, et leida 95.

$$95-19\sqrt{3}\sqrt{5}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{3} ja \sqrt{5} korrutage numbrid, mis on sama juur.

$$95-19\sqrt{15}-19\sqrt{5}\sqrt{2}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{5} ja \sqrt{2} korrutage numbrid, mis on sama juur.

$$95-19\sqrt{15}-19\sqrt{10}-19\sqrt{3}\sqrt{5}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{3} ja \sqrt{5} korrutage numbrid, mis on sama juur.

$$95-19\sqrt{15}-19\sqrt{10}-19\sqrt{15}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Kombineerige -19\sqrt{15} ja -19\sqrt{15}, et leida -38\sqrt{15}.

$$95-38\sqrt{15}-19\sqrt{10}+19\left(\sqrt{3}\right)^{2}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{3} ruut on 3.

$$95-38\sqrt{15}-19\sqrt{10}+19\times 3+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Korrutage 19 ja 3, et leida 57.

$$95-38\sqrt{15}-19\sqrt{10}+57+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Liitke 95 ja 57, et leida 152.

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{3}\sqrt{2}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

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

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{6}+19\sqrt{2}\sqrt{5}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{2} ja \sqrt{5} korrutage numbrid, mis on sama juur.

$$152-38\sqrt{15}-19\sqrt{10}+19\sqrt{6}+19\sqrt{10}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

Kombineerige -19\sqrt{10} ja 19\sqrt{10}, et leida 0.

$$152-38\sqrt{15}+19\sqrt{6}-19\sqrt{3}\sqrt{2}-19\left(\sqrt{2}\right)^{2}$$

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

$$152-38\sqrt{15}+19\sqrt{6}-19\sqrt{6}-19\left(\sqrt{2}\right)^{2}$$

Kombineerige 19\sqrt{6} ja -19\sqrt{6}, et leida 0.

$$152-38\sqrt{15}-19\left(\sqrt{2}\right)^{2}$$

\sqrt{2} ruut on 2.

$$152-38\sqrt{15}-19\times 2$$

Korrutage -19 ja 2, et leida -38.

$$152-38\sqrt{15}-38$$

Lahutage 38 väärtusest 152, et leida 114.

$$114-38\sqrt{15}$$