Lahenda fx^2+y^2-2x-6y+5=0

$$f x ^ { 2 } + y ^ { 2 } - 2 x - 6 y + 5 = 0$$

Lahendage ja leidke f (complex solution)

$$\left\{\begin{matrix}f=-\frac{5-6y+y^{2}-2x}{x^{2}}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&\left(y=5\text{ or }y=1\right)\text{ and }x=0\end{matrix}\right,$$

Juhised lineaarvõrrandi lahendamiseks

Lahutage mõlemast poolest y^{2}. Mis tahes arvu lahutamisel nullist on tulemuseks sama arvu negatiivne väärtus.

$$fx^{2}-2x-6y+5=-y^{2}$$

Liitke 2x mõlemale poolele.

$$fx^{2}-6y+5=-y^{2}+2x$$

Liitke 6y mõlemale poolele.

$$fx^{2}+5=-y^{2}+2x+6y$$

Lahutage mõlemast poolest 5.

$$fx^{2}=-y^{2}+2x+6y-5$$

Võrrand on standardkujul.

$$x^{2}f=2x-y^{2}+6y-5$$

Jagage mõlemad pooled x^{2}-ga.

$$\frac{x^{2}f}{x^{2}}=\frac{2x-y^{2}+6y-5}{x^{2}}$$

x^{2}-ga jagamine võtab x^{2}-ga korrutamise tagasi.

$$f=\frac{2x-y^{2}+6y-5}{x^{2}}$$

Lahendage ja leidke f

$$\left\{\begin{matrix}f=-\frac{5-6y+y^{2}-2x}{x^{2}}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&\left(y=5\text{ or }y=1\right)\text{ and }x=0\end{matrix}\right,$$

Juhised lineaarvõrrandi lahendamiseks

Lahutage mõlemast poolest y^{2}. Mis tahes arvu lahutamisel nullist on tulemuseks sama arvu negatiivne väärtus.

$$fx^{2}-2x-6y+5=-y^{2}$$

Liitke 2x mõlemale poolele.

$$fx^{2}-6y+5=-y^{2}+2x$$

Liitke 6y mõlemale poolele.

$$fx^{2}+5=-y^{2}+2x+6y$$

Lahutage mõlemast poolest 5.

$$fx^{2}=-y^{2}+2x+6y-5$$

Võrrand on standardkujul.

$$x^{2}f=2x-y^{2}+6y-5$$

Jagage mõlemad pooled x^{2}-ga.

$$\frac{x^{2}f}{x^{2}}=\frac{2x-y^{2}+6y-5}{x^{2}}$$

x^{2}-ga jagamine võtab x^{2}-ga korrutamise tagasi.

$$f=\frac{2x-y^{2}+6y-5}{x^{2}}$$

Lahendage ja leidke x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{1-5f+6fy-fy^{2}}+1}{f}\text{; }x=\frac{-\sqrt{1-5f+6fy-fy^{2}}+1}{f}\text{, }&f\neq 0\\x=\frac{\left(y-5\right)\left(y-1\right)}{2}\text{, }&f=0\end{matrix}\right,$$

Lahendage ja leidke x

$$\left\{\begin{matrix}x=\frac{\sqrt{1-5f+6fy-fy^{2}}+1}{f}\text{; }x=\frac{-\sqrt{1-5f+6fy-fy^{2}}+1}{f}\text{, }&\left(f\neq 0\text{ and }y=1\right)\text{ or }\left(f\neq 0\text{ and }y\leq 1\text{ and }f\leq -\frac{1}{-y^{2}+6y-5}\right)\text{ or }\left(f\neq 0\text{ and }y=5\right)\text{ or }\left(f\neq 0\text{ and }y\geq 5\text{ and }f\leq -\frac{1}{-y^{2}+6y-5}\right)\text{ or }\left(f\neq 0\text{ and }f\geq -\frac{1}{-y^{2}+6y-5}\text{ and }y\geq 1\text{ and }y\leq 5\right)\text{ or }\left(y\neq 1\text{ and }y\neq 5\text{ and }f=-\frac{1}{-y^{2}+6y-5}\right)\\x=\frac{\left(y-5\right)\left(y-1\right)}{2}\text{, }&f=0\end{matrix}\right,$$