(x+1)*(x+3)=x^2+13cm^2 eching

$$( x + 1 ) \cdot ( x + 3 ) = x ^ { 2 } + 13 cm ^ { 2 }$$

c uchun yechish (complex solution)

$$\left\{\begin{matrix}c=\frac{4x+3}{13m^{2}}\text{, }&m\neq 0\\c\in \mathrm{C}\text{, }&x=-\frac{3}{4}\text{ and }m=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x+1 ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+4x+3=x^{2}+13cm^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+13cm^{2}=x^{2}+4x+3$$

Ikkala tarafdan x^{2} ni ayirish.

$$13cm^{2}=x^{2}+4x+3-x^{2}$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$13cm^{2}=4x+3$$

Tenglama standart shaklda.

$$13m^{2}c=4x+3$$

Ikki tarafini 13m^{2} ga bo‘ling.

$$\frac{13m^{2}c}{13m^{2}}=\frac{4x+3}{13m^{2}}$$

13m^{2} ga bo'lish 13m^{2} ga ko'paytirishni bekor qiladi.

$$c=\frac{4x+3}{13m^{2}}$$

c uchun yechish

$$\left\{\begin{matrix}c=\frac{4x+3}{13m^{2}}\text{, }&m\neq 0\\c\in \mathrm{R}\text{, }&x=-\frac{3}{4}\text{ and }m=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x+1 ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+4x+3=x^{2}+13cm^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+13cm^{2}=x^{2}+4x+3$$

Ikkala tarafdan x^{2} ni ayirish.

$$13cm^{2}=x^{2}+4x+3-x^{2}$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$13cm^{2}=4x+3$$

Tenglama standart shaklda.

$$13m^{2}c=4x+3$$

Ikki tarafini 13m^{2} ga bo‘ling.

$$\frac{13m^{2}c}{13m^{2}}=\frac{4x+3}{13m^{2}}$$

13m^{2} ga bo'lish 13m^{2} ga ko'paytirishni bekor qiladi.

$$c=\frac{4x+3}{13m^{2}}$$

m uchun yechish (complex solution)

$$\left\{\begin{matrix}m=-\frac{ic^{-\frac{1}{2}}\sqrt{-52x-39}}{13}\text{; }m=\frac{ic^{-\frac{1}{2}}\sqrt{-52x-39}}{13}\text{, }&c\neq 0\\m\in \mathrm{C}\text{, }&x=-\frac{3}{4}\text{ and }c=0\end{matrix}\right,$$

m uchun yechish

$$\left\{\begin{matrix}m=\frac{\sqrt{\frac{13\left(4x+3\right)}{c}}}{13}\text{; }m=-\frac{\sqrt{\frac{13\left(4x+3\right)}{c}}}{13}\text{, }&\left(x\geq -\frac{3}{4}\text{ and }c>0\right)\text{ or }\left(x\leq -\frac{3}{4}\text{ and }c<0\right)\\m\in \mathrm{R}\text{, }&x=-\frac{3}{4}\text{ and }c=0\end{matrix}\right,$$