x_1 uchun yechish (complex solution)
\left\{\begin{matrix}x_{1}=\frac{y}{\left(x-3\right)^{2}}\text{, }&x\neq 3\\x_{1}\in \mathrm{C}\text{, }&y=0\text{ and }x=3\end{matrix}\right,
x_1 uchun yechish
\left\{\begin{matrix}x_{1}=\frac{y}{\left(x-3\right)^{2}}\text{, }&x\neq 3\\x_{1}\in \mathrm{R}\text{, }&y=0\text{ and }x=3\end{matrix}\right,
x uchun yechish (complex solution)
\left\{\begin{matrix}x=3+x_{1}^{-\frac{1}{2}}\sqrt{y}\text{; }x=3-x_{1}^{-\frac{1}{2}}\sqrt{y}\text{, }&x_{1}\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }x_{1}=0\end{matrix}\right,
x uchun yechish
\left\{\begin{matrix}x=-\sqrt{\frac{y}{x_{1}}}+3\text{; }x=\sqrt{\frac{y}{x_{1}}}+3\text{, }&y\leq 0\text{ and }x_{1}<0\\x=-\sqrt{\frac{y}{x_{1}}}+3\text{; }x=\sqrt{\frac{y}{x_{1}}}+3\text{, }&y\geq 0\text{ and }x_{1}>0\\x\in \mathrm{R}\text{, }&y=0\text{ and }x_{1}=0\end{matrix}\right,
Grafik
Baham ko'rish
Klipbordga nusxa olish
y=\left(x^{2}-6x+9\right)x_{1}
\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-3\right)^{2} kengaytirilishi uchun ishlating.
y=x^{2}x_{1}-6xx_{1}+9x_{1}
x^{2}-6x+9 ga x_{1} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
x^{2}x_{1}-6xx_{1}+9x_{1}=y
Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.
\left(x^{2}-6x+9\right)x_{1}=y
x_{1}'ga ega bo'lgan barcha shartlarni birlashtirish.
\frac{\left(x^{2}-6x+9\right)x_{1}}{x^{2}-6x+9}=\frac{y}{x^{2}-6x+9}
Ikki tarafini x^{2}-6x+9 ga bo‘ling.
x_{1}=\frac{y}{x^{2}-6x+9}
x^{2}-6x+9 ga bo'lish x^{2}-6x+9 ga ko'paytirishni bekor qiladi.
x_{1}=\frac{y}{\left(x-3\right)^{2}}
y ni x^{2}-6x+9 ga bo'lish.
y=\left(x^{2}-6x+9\right)x_{1}
\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-3\right)^{2} kengaytirilishi uchun ishlating.
y=x^{2}x_{1}-6xx_{1}+9x_{1}
x^{2}-6x+9 ga x_{1} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
x^{2}x_{1}-6xx_{1}+9x_{1}=y
Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.
\left(x^{2}-6x+9\right)x_{1}=y
x_{1}'ga ega bo'lgan barcha shartlarni birlashtirish.
\frac{\left(x^{2}-6x+9\right)x_{1}}{x^{2}-6x+9}=\frac{y}{x^{2}-6x+9}
Ikki tarafini x^{2}-6x+9 ga bo‘ling.
x_{1}=\frac{y}{x^{2}-6x+9}
x^{2}-6x+9 ga bo'lish x^{2}-6x+9 ga ko'paytirishni bekor qiladi.
x_{1}=\frac{y}{\left(x-3\right)^{2}}
y ni x^{2}-6x+9 ga bo'lish.
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