Atrisiniet x+sqrt{265}+y+45+13/y=17

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

Atrast x

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

$$y\neq 0$$

Lineāra vienādojuma risināšanas darbības

Reiziniet vienādojuma abas puses ar y.

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

Reiziniet y un y, lai iegūtu y^{2}.

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

Atņemiet y\sqrt{265} no abām pusēm.

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

Atņemiet y^{2} no abām pusēm.

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

Atņemiet y\times 45 no abām pusēm.

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

Atņemiet 13 no abām pusēm.

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

Reiziniet -1 un 45, lai iegūtu -45.

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

Savelciet 17y un -45y, lai iegūtu -28y.

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

Vienādojums ir standarta formā.

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

Daliet abas puses ar y.

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

Dalīšana ar y atsauc reizināšanu ar y.

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

Daliet -28y-y\sqrt{265}-y^{2}-13 ar y.

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

Atrast y (complex solution)

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

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

Atrast y

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

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