Resolver z=u^2v+uv

$$z = u ^ { 2 } v + u v$$

Ebatzi: v (complex solution)

$$\left\{\begin{matrix}v=\frac{z}{u\left(u+1\right)}\text{, }&u\neq -1\text{ and }u\neq 0\\v\in \mathrm{C}\text{, }&\left(u=0\text{ or }u=-1\right)\text{ and }z=0\end{matrix}\right.$$

Ekuazio lineala ebazteko urratsak

Trukatu aldeak, aldagaiak ezkerraldean egon daitezen.

$$u^{2}v+uv=z$$

Konbinatu v duten gai guztiak.

$$\left(u^{2}+u\right)v=z$$

Zatitu ekuazioaren bi aldeak u^{2}+u balioarekin.

$$\frac{\left(u^{2}+u\right)v}{u^{2}+u}=\frac{z}{u^{2}+u}$$

u^{2}+u balioarekin zatituz gero, u^{2}+u balioarekiko biderketa desegiten da.

$$v=\frac{z}{u^{2}+u}$$

Zatitu z balioa u^{2}+u balioarekin.

$$v=\frac{z}{u\left(u+1\right)}$$

Ebatzi: v

$$\left\{\begin{matrix}v=\frac{z}{u\left(u+1\right)}\text{, }&u\neq -1\text{ and }u\neq 0\\v\in \mathrm{R}\text{, }&\left(u=0\text{ or }u=-1\right)\text{ and }z=0\end{matrix}\right.$$

Ekuazio lineala ebazteko urratsak

Trukatu aldeak, aldagaiak ezkerraldean egon daitezen.

$$u^{2}v+uv=z$$

Konbinatu v duten gai guztiak.

$$\left(u^{2}+u\right)v=z$$

Zatitu ekuazioaren bi aldeak u^{2}+u balioarekin.

$$\frac{\left(u^{2}+u\right)v}{u^{2}+u}=\frac{z}{u^{2}+u}$$

u^{2}+u balioarekin zatituz gero, u^{2}+u balioarekiko biderketa desegiten da.

$$v=\frac{z}{u^{2}+u}$$

Zatitu z balioa u^{2}+u balioarekin.

$$v=\frac{z}{u\left(u+1\right)}$$

Ebatzi: u (complex solution)

$$\left\{\begin{matrix}u=-\frac{\sqrt{v\left(4z+v\right)}+v}{2v}\text{; }u=-\frac{-\sqrt{v\left(4z+v\right)}+v}{2v}\text{, }&v\neq 0\\u\in \mathrm{C}\text{, }&v=0\text{ and }z=0\end{matrix}\right.$$

Ebatzi: u

$$\left\{\begin{matrix}u=-\frac{\sqrt{v\left(4z+v\right)}+v}{2v}\text{; }u=-\frac{-\sqrt{v\left(4z+v\right)}+v}{2v}\text{, }&\left(z\leq -\frac{v}{4}\text{ and }v<0\right)\text{ or }\left(z\geq -\frac{v}{4}\text{ and }v>0\right)\text{ or }\left(v\neq 0\text{ and }z=-\frac{v}{4}\right)\\u\in \mathrm{R}\text{, }&v=0\text{ and }z=0\end{matrix}\right.$$