yx^2-160x-36=0 eching

$$y x ^ { 2 } - 160 x - 36 = 0$$

y uchun yechish

$$y=\frac{4\left(40x+9\right)}{x^{2}}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

160x ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$yx^{2}-36=160x$$

36 ni ikki tarafga qo’shing.

$$yx^{2}=160x+36$$

Tenglama standart shaklda.

$$x^{2}y=160x+36$$

Ikki tarafini x^{2} ga bo‘ling.

$$\frac{x^{2}y}{x^{2}}=\frac{160x+36}{x^{2}}$$

x^{2} ga bo'lish x^{2} ga ko'paytirishni bekor qiladi.

$$y=\frac{160x+36}{x^{2}}$$

160x+36 ni x^{2} ga bo'lish.

$$y=\frac{4\left(40x+9\right)}{x^{2}}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{2\left(\sqrt{9y+1600}+40\right)}{y}\text{; }x=\frac{2\left(-\sqrt{9y+1600}+40\right)}{y}\text{, }&y\neq 0\\x=-\frac{9}{40}=-0,225\text{, }&y=0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{2\left(\sqrt{9y+1600}+40\right)}{y}\text{; }x=\frac{2\left(-\sqrt{9y+1600}+40\right)}{y}\text{, }&y\neq 0\text{ and }y\geq -\frac{1600}{9}\\x=-\frac{9}{40}=-0,225\text{, }&y=0\end{matrix}\right,$$