Riješi alphabeta^2+alpha^2beta=alphabeta(alpha+beta)

$$\alpha \beta ^ { 2 } + \alpha ^ { 2 } \beta = \alpha \beta ( \alpha + \beta )$$

Izračunaj α (complex solution)

$$\alpha \in \mathrm{C}$$

Koraci rješenja

Koristite svojstvo distributivnosti da biste pomnožili \alpha \beta s \alpha +\beta .

$$\alpha \beta ^{2}+\alpha ^{2}\beta =\beta \alpha ^{2}+\alpha \beta ^{2}$$

Oduzmite \beta \alpha ^{2} od obiju strana.

$$\alpha \beta ^{2}+\alpha ^{2}\beta -\beta \alpha ^{2}=\alpha \beta ^{2}$$

Kombinirajte \alpha ^{2}\beta i -\beta \alpha ^{2} da biste dobili 0.

$$\alpha \beta ^{2}=\alpha \beta ^{2}$$

Oduzmite \alpha \beta ^{2} od obiju strana.

$$\alpha \beta ^{2}-\alpha \beta ^{2}=0$$

Kombinirajte \alpha \beta ^{2} i -\alpha \beta ^{2} da biste dobili 0.

$$0=0$$

Usporedite 0 i 0.

$$\text{true}$$

To vrijedi za svaki \alpha .

$$\alpha \in \mathrm{C}$$

Izračunaj β (complex solution)

$$\beta \in \mathrm{C}$$

Koraci rješenja

Koristite svojstvo distributivnosti da biste pomnožili \alpha \beta s \alpha +\beta .

$$\alpha \beta ^{2}+\alpha ^{2}\beta =\beta \alpha ^{2}+\alpha \beta ^{2}$$

Oduzmite \beta \alpha ^{2} od obiju strana.

$$\alpha \beta ^{2}+\alpha ^{2}\beta -\beta \alpha ^{2}=\alpha \beta ^{2}$$

Kombinirajte \alpha ^{2}\beta i -\beta \alpha ^{2} da biste dobili 0.

$$\alpha \beta ^{2}=\alpha \beta ^{2}$$

Oduzmite \alpha \beta ^{2} od obiju strana.

$$\alpha \beta ^{2}-\alpha \beta ^{2}=0$$

Kombinirajte \alpha \beta ^{2} i -\alpha \beta ^{2} da biste dobili 0.

$$0=0$$

Usporedite 0 i 0.

$$\text{true}$$

To vrijedi za svaki \beta .

$$\beta \in \mathrm{C}$$

Izračunaj α

$$\alpha \in \mathrm{R}$$

Koraci rješenja

Koristite svojstvo distributivnosti da biste pomnožili \alpha \beta s \alpha +\beta .

$$\alpha \beta ^{2}+\alpha ^{2}\beta =\beta \alpha ^{2}+\alpha \beta ^{2}$$

Oduzmite \beta \alpha ^{2} od obiju strana.

$$\alpha \beta ^{2}+\alpha ^{2}\beta -\beta \alpha ^{2}=\alpha \beta ^{2}$$

Kombinirajte \alpha ^{2}\beta i -\beta \alpha ^{2} da biste dobili 0.

$$\alpha \beta ^{2}=\alpha \beta ^{2}$$

Oduzmite \alpha \beta ^{2} od obiju strana.

$$\alpha \beta ^{2}-\alpha \beta ^{2}=0$$

Kombinirajte \alpha \beta ^{2} i -\alpha \beta ^{2} da biste dobili 0.

$$0=0$$

Usporedite 0 i 0.

$$\text{true}$$

To vrijedi za svaki \alpha .

$$\alpha \in \mathrm{R}$$

Izračunaj β

$$\beta \in \mathrm{R}$$

Koraci rješenja

Koristite svojstvo distributivnosti da biste pomnožili \alpha \beta s \alpha +\beta .

$$\alpha \beta ^{2}+\alpha ^{2}\beta =\beta \alpha ^{2}+\alpha \beta ^{2}$$

Oduzmite \beta \alpha ^{2} od obiju strana.

$$\alpha \beta ^{2}+\alpha ^{2}\beta -\beta \alpha ^{2}=\alpha \beta ^{2}$$

Kombinirajte \alpha ^{2}\beta i -\beta \alpha ^{2} da biste dobili 0.

$$\alpha \beta ^{2}=\alpha \beta ^{2}$$

Oduzmite \alpha \beta ^{2} od obiju strana.

$$\alpha \beta ^{2}-\alpha \beta ^{2}=0$$

Kombinirajte \alpha \beta ^{2} i -\alpha \beta ^{2} da biste dobili 0.

$$0=0$$

Usporedite 0 i 0.

$$\text{true}$$

To vrijedi za svaki \beta .

$$\beta \in \mathrm{R}$$