Resolver y/left(0.01(x-105)right)^2=z

$$\frac{ y }{ { \left(0.01(x-105) \right) }^{ 2 } } =z$$

Ebatzi: y

$$y=\frac{z\left(x-105\right)^{2}}{10000}$$

$$x\neq 105$$

Ekuazio lineala ebazteko urratsak

Garatu \left(0.01\left(x-105\right)\right)^{2}.

$$\frac{y}{0.01^{2}\left(x-105\right)^{2}}=z$$

0.0001 lortzeko, egin 0.01 ber 2.

$$\frac{y}{0.0001\left(x-105\right)^{2}}=z$$

\left(x-105\right)^{2} zabaltzeko, erabili Newton-en binomioa \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

$$\frac{y}{0.0001\left(x^{2}-210x+11025\right)}=z$$

Erabili banaketa-propietatea 0.0001 eta x^{2}-210x+11025 biderkatzeko.

$$\frac{y}{0.0001x^{2}-0.021x+1.1025}=z$$

Modu arruntean dago ekuazioa.

$$\frac{1}{\frac{x^{2}}{10000}-\frac{21x}{1000}+1.1025}y=z$$

Zatitu ekuazioaren bi aldeak \left(0.0001x^{2}-0.021x+1.1025\right)^{-1} balioarekin.

$$\frac{\frac{1}{\frac{x^{2}}{10000}-\frac{21x}{1000}+1.1025}y\left(\frac{x^{2}}{10000}-\frac{21x}{1000}+1.1025\right)}{1}=\frac{z\left(\frac{x^{2}}{10000}-\frac{21x}{1000}+1.1025\right)}{1}$$

\left(0.0001x^{2}-0.021x+1.1025\right)^{-1} balioarekin zatituz gero, \left(0.0001x^{2}-0.021x+1.1025\right)^{-1} balioarekiko biderketa desegiten da.

$$y=\frac{z\left(\frac{x^{2}}{10000}-\frac{21x}{1000}+1.1025\right)}{1}$$

Zatitu z balioa \left(0.0001x^{2}-0.021x+1.1025\right)^{-1} balioarekin.

$$y=\frac{z\left(x-105\right)^{2}}{10000}$$

Ebatzi: x (complex solution)

$$\left\{\begin{matrix}\\x\neq 105\text{, }&\text{unconditionally}\\x=-100z^{-0.5}\sqrt{y}+105\text{; }x=100z^{-0.5}\sqrt{y}+105\text{, }&y\neq 0\text{ and }z\neq 0\end{matrix}\right.$$

Ebatzi: x

$$\left\{\begin{matrix}\\x\neq 105\text{, }&\text{unconditionally}\\x=-100\sqrt{\frac{y}{z}}+105\text{; }x=100\sqrt{\frac{y}{z}}+105\text{, }&z>0\text{ and }y>0\\x=-100\sqrt{\frac{y}{z}}+105\text{; }x=100\sqrt{\frac{y}{z}}+105\text{, }&z<0\text{ and }y<0\end{matrix}\right.$$