Issolvi AR^2+PB^2=PR^2+AB^2

$$A R ^ { 2 } + P B ^ { 2 } = P R ^ { 2 } + A B ^ { 2 }$$

Solvi għal A (complex solution)

$$\left\{\begin{matrix}\\A=P\text{, }&\text{unconditionally}\\A\in \mathrm{C}\text{, }&R=-B\text{ or }R=B\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Naqqas AB^{2} miż-żewġ naħat.

$$AR^{2}+PB^{2}-AB^{2}=PR^{2}$$

Naqqas PB^{2} miż-żewġ naħat.

$$AR^{2}-AB^{2}=PR^{2}-PB^{2}$$

Ikkombina t-termini kollha li fihom A.

$$\left(R^{2}-B^{2}\right)A=PR^{2}-PB^{2}$$

Iddividi ż-żewġ naħat b'R^{2}-B^{2}.

$$\frac{\left(R^{2}-B^{2}\right)A}{R^{2}-B^{2}}=\frac{P\left(R-B\right)\left(B+R\right)}{R^{2}-B^{2}}$$

Meta tiddividi b'R^{2}-B^{2} titneħħa l-multiplikazzjoni b'R^{2}-B^{2}.

$$A=\frac{P\left(R-B\right)\left(B+R\right)}{R^{2}-B^{2}}$$

Iddividi P\left(R-B\right)\left(R+B\right) b'R^{2}-B^{2}.

$$A=P$$

Solvi għal A

$$\left\{\begin{matrix}\\A=P\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&|R|=|B|\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Naqqas AB^{2} miż-żewġ naħat.

$$AR^{2}+PB^{2}-AB^{2}=PR^{2}$$

Naqqas PB^{2} miż-żewġ naħat.

$$AR^{2}-AB^{2}=PR^{2}-PB^{2}$$

Ikkombina t-termini kollha li fihom A.

$$\left(R^{2}-B^{2}\right)A=PR^{2}-PB^{2}$$

Iddividi ż-żewġ naħat b'R^{2}-B^{2}.

$$\frac{\left(R^{2}-B^{2}\right)A}{R^{2}-B^{2}}=\frac{P\left(R-B\right)\left(B+R\right)}{R^{2}-B^{2}}$$

Meta tiddividi b'R^{2}-B^{2} titneħħa l-multiplikazzjoni b'R^{2}-B^{2}.

$$A=\frac{P\left(R-B\right)\left(B+R\right)}{R^{2}-B^{2}}$$

Iddividi P\left(R-B\right)\left(R+B\right) b'R^{2}-B^{2}.

$$A=P$$

Solvi għal B (complex solution)

$$\left\{\begin{matrix}\\B=-R\text{; }B=R\text{, }&\text{unconditionally}\\B\in \mathrm{C}\text{, }&A=P\end{matrix}\right.$$

Solvi għal B

$$\left\{\begin{matrix}\\B=-R\text{; }B=R\text{, }&\text{unconditionally}\\B\in \mathrm{R}\text{, }&A=P\end{matrix}\right.$$