Løs x+sqrt{265}+y+45+13/y=17

$$x + \sqrt { 265 } + y + 45 + \frac { 13 } { y } = 17$$

Løs for x

$$x=-y-\sqrt{265}-28-\frac{13}{y}$$

$$y\neq 0$$

Vejledning i at løse lineær ligning

Multiplicer begge sider af ligningen med y.

$$yx+y\sqrt{265}+yy+y\times 45+13=17y$$

Multiplicer y og y for at få y^{2}.

$$yx+y\sqrt{265}+y^{2}+y\times 45+13=17y$$

Subtraher y\sqrt{265} fra begge sider.

$$yx+y^{2}+y\times 45+13=17y-y\sqrt{265}$$

Subtraher y^{2} fra begge sider.

$$yx+y\times 45+13=17y-y\sqrt{265}-y^{2}$$

Subtraher y\times 45 fra begge sider.

$$yx+13=17y-y\sqrt{265}-y^{2}-y\times 45$$

Subtraher 13 fra begge sider.

$$yx=17y-y\sqrt{265}-y^{2}-y\times 45-13$$

Multiplicer -1 og 45 for at få -45.

$$yx=17y-y\sqrt{265}-y^{2}-45y-13$$

Kombiner 17y og -45y for at få -28y.

$$yx=-28y-y\sqrt{265}-y^{2}-13$$

Ligningen er nu i standardform.

$$yx=-y^{2}-\sqrt{265}y-28y-13$$

Divider begge sider med y.

$$\frac{yx}{y}=\frac{-y^{2}-\sqrt{265}y-28y-13}{y}$$

Division med y annullerer multiplikationen med y.

$$x=\frac{-y^{2}-\sqrt{265}y-28y-13}{y}$$

Divider -28y-y\sqrt{265}-y^{2}-13 med y.

$$x=-y-\sqrt{265}-28-\frac{13}{y}$$

Løs for y (complex solution)

$$y=\frac{\sqrt{x^{2}+2\sqrt{265}x+56x+56\sqrt{265}+997}}{2}-\frac{x}{2}-\frac{\sqrt{265}}{2}-14$$

$$y=-\frac{\sqrt{x^{2}+2\sqrt{265}x+56x+56\sqrt{265}+997}}{2}-\frac{x}{2}-\frac{\sqrt{265}}{2}-14$$

Løs for y

$$y=\frac{\sqrt{x^{2}+2\sqrt{265}x+56x+56\sqrt{265}+997}}{2}-\frac{x}{2}-\frac{\sqrt{265}}{2}-14$$

$$y=-\frac{\sqrt{x^{2}+2\sqrt{265}x+56x+56\sqrt{265}+997}}{2}-\frac{x}{2}-\frac{\sqrt{265}}{2}-14\text{, }x\geq 2\sqrt{13}-\sqrt{265}-28\text{ or }x\leq -\sqrt{265}-2\sqrt{13}-28$$