Atrisiniet ty^2-48y+18=9

$$t y ^ { 2 } - 48 y + 18 = 9$$

Atrast t

$$t=-\frac{3\left(3-16y\right)}{y^{2}}$$

$$y\neq 0$$

Lineāra vienādojuma risināšanas darbības

Pievienot 48y abās pusēs.

$$ty^{2}+18=9+48y$$

Atņemiet 18 no abām pusēm.

$$ty^{2}=9+48y-18$$

Atņemiet 18 no 9, lai iegūtu -9.

$$ty^{2}=-9+48y$$

Vienādojums ir standarta formā.

$$y^{2}t=48y-9$$

Daliet abas puses ar y^{2}.

$$\frac{y^{2}t}{y^{2}}=\frac{48y-9}{y^{2}}$$

Dalīšana ar y^{2} atsauc reizināšanu ar y^{2}.

$$t=\frac{48y-9}{y^{2}}$$

Daliet -9+48y ar y^{2}.

$$t=\frac{3\left(16y-3\right)}{y^{2}}$$

Atrast y (complex solution)

$$\left\{\begin{matrix}y=\frac{3\left(\sqrt{64-t}+8\right)}{t}\text{; }y=\frac{3\left(-\sqrt{64-t}+8\right)}{t}\text{, }&t\neq 0\\y=\frac{3}{16}\text{, }&t=0\end{matrix}\right,$$

Atrast y

$$\left\{\begin{matrix}y=\frac{3\left(\sqrt{64-t}+8\right)}{t}\text{; }y=\frac{3\left(-\sqrt{64-t}+8\right)}{t}\text{, }&t\neq 0\text{ and }t\leq 64\\y=\frac{3}{16}\text{, }&t=0\end{matrix}\right,$$