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

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

Izrēķināt

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

Atrisinājuma darbības

Izmantojiet distributīvo īpašību, lai reizinātu 19 ar \sqrt{5}-\sqrt{3}+\sqrt{2}.

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

Izmantojiet distributīvo īpašību, katru 19\sqrt{5}-19\sqrt{3}+19\sqrt{2} locekli reizinot ar katru \sqrt{5}-\sqrt{3}-\sqrt{2} locekli.

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

Skaitļa \sqrt{5} kvadrāts ir 5.

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

Reiziniet 19 un 5, lai iegūtu 95.

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

Lai reiziniet \sqrt{3} un \sqrt{5}, reiziniet numurus zem kvadrātveida saknes.

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

Lai reiziniet \sqrt{5} un \sqrt{2}, reiziniet numurus zem kvadrātveida saknes.

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

Lai reiziniet \sqrt{3} un \sqrt{5}, reiziniet numurus zem kvadrātveida saknes.

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

Savelciet -19\sqrt{15} un -19\sqrt{15}, lai iegūtu -38\sqrt{15}.

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

Skaitļa \sqrt{3} kvadrāts ir 3.

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

Reiziniet 19 un 3, lai iegūtu 57.

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

Saskaitiet 95 un 57, lai iegūtu 152.

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

Lai reiziniet \sqrt{3} un \sqrt{2}, reiziniet numurus zem kvadrātveida saknes.

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

Lai reiziniet \sqrt{2} un \sqrt{5}, reiziniet numurus zem kvadrātveida saknes.

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

Savelciet -19\sqrt{10} un 19\sqrt{10}, lai iegūtu 0.

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

Lai reiziniet \sqrt{3} un \sqrt{2}, reiziniet numurus zem kvadrātveida saknes.

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

Savelciet 19\sqrt{6} un -19\sqrt{6}, lai iegūtu 0.

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

Skaitļa \sqrt{2} kvadrāts ir 2.

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

Reiziniet -19 un 2, lai iegūtu -38.

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

Atņemiet 38 no 152, lai iegūtu 114.

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