y=m(x-3)^2 eching

$$y = m ( x - 3 ) ^ { 2 }$$

m uchun yechish (complex solution)

$$\left\{\begin{matrix}m=\frac{y}{\left(x-3\right)^{2}}\text{, }&x\neq 3\\m\in \mathrm{C}\text{, }&y=0\text{ and }x=3\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-3\right)^{2} kengaytirilishi uchun ishlating.

$$y=m\left(x^{2}-6x+9\right)$$

m ga x^{2}-6x+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y=mx^{2}-6mx+9m$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$mx^{2}-6mx+9m=y$$

m'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-6x+9\right)m=y$$

Ikki tarafini x^{2}-6x+9 ga bo‘ling.

$$\frac{\left(x^{2}-6x+9\right)m}{x^{2}-6x+9}=\frac{y}{x^{2}-6x+9}$$

x^{2}-6x+9 ga bo'lish x^{2}-6x+9 ga ko'paytirishni bekor qiladi.

$$m=\frac{y}{x^{2}-6x+9}$$

y ni x^{2}-6x+9 ga bo'lish.

$$m=\frac{y}{\left(x-3\right)^{2}}$$

m uchun yechish

$$\left\{\begin{matrix}m=\frac{y}{\left(x-3\right)^{2}}\text{, }&x\neq 3\\m\in \mathrm{R}\text{, }&y=0\text{ and }x=3\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-3\right)^{2} kengaytirilishi uchun ishlating.

$$y=m\left(x^{2}-6x+9\right)$$

m ga x^{2}-6x+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y=mx^{2}-6mx+9m$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$mx^{2}-6mx+9m=y$$

m'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-6x+9\right)m=y$$

Ikki tarafini x^{2}-6x+9 ga bo‘ling.

$$\frac{\left(x^{2}-6x+9\right)m}{x^{2}-6x+9}=\frac{y}{x^{2}-6x+9}$$

x^{2}-6x+9 ga bo'lish x^{2}-6x+9 ga ko'paytirishni bekor qiladi.

$$m=\frac{y}{x^{2}-6x+9}$$

y ni x^{2}-6x+9 ga bo'lish.

$$m=\frac{y}{\left(x-3\right)^{2}}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=3+m^{-\frac{1}{2}}\sqrt{y}\text{; }x=3-m^{-\frac{1}{2}}\sqrt{y}\text{, }&m\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }m=0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=-\sqrt{\frac{y}{m}}+3\text{; }x=\sqrt{\frac{y}{m}}+3\text{, }&y\leq 0\text{ and }m<0\\x=-\sqrt{\frac{y}{m}}+3\text{; }x=\sqrt{\frac{y}{m}}+3\text{, }&y\geq 0\text{ and }m>0\\x\in \mathrm{R}\text{, }&y=0\text{ and }m=0\end{matrix}\right,$$