x^2+mx+n/x^2-7x+10=x+1/x-5Rightarrowm+n=? eching

$$\frac { x ^ { 2 } + m x + n } { x ^ { 2 } - 7 x + 10 } = \frac { x + 1 } { x - 5 } \Rightarrow m + n = ?$$

m uchun yechish (complex solution)

$$\left\{\begin{matrix}m=-\frac{x+n+2}{x}\text{, }&x\neq 0\text{ and }x\neq 2\text{ and }x\neq 5\\m\in \mathrm{C}\text{, }&x=0\text{ and }n=-2\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini \left(x-5\right)\left(x-2\right) ga, x^{2}-7x+10,x-5 ning eng kichik karralisiga ko‘paytiring.

$$x^{2}+mx+n=\left(x-2\right)\left(x+1\right)$$

x-2 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+mx+n=x^{2}-x-2$$

Ikkala tarafdan x^{2} ni ayirish.

$$mx+n=x^{2}-x-2-x^{2}$$

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

$$mx+n=-x-2$$

Ikkala tarafdan n ni ayirish.

$$mx=-x-2-n$$

Tenglama standart shaklda.

$$xm=-x-n-2$$

Ikki tarafini x ga bo‘ling.

$$\frac{xm}{x}=\frac{-x-n-2}{x}$$

x ga bo'lish x ga ko'paytirishni bekor qiladi.

$$m=\frac{-x-n-2}{x}$$

-x-2-n ni x ga bo'lish.

$$m=-\frac{x+n+2}{x}$$

n uchun yechish (complex solution)

$$n=-\left(mx+x+2\right)$$

$$x\neq 2\text{ and }x\neq 5$$

Yechim qadamlari

Tenglamaning ikkala tarafini \left(x-5\right)\left(x-2\right) ga, x^{2}-7x+10,x-5 ning eng kichik karralisiga ko‘paytiring.

$$x^{2}+mx+n=\left(x-2\right)\left(x+1\right)$$

x-2 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+mx+n=x^{2}-x-2$$

Ikkala tarafdan x^{2} ni ayirish.

$$mx+n=x^{2}-x-2-x^{2}$$

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

$$mx+n=-x-2$$

Ikkala tarafdan mx ni ayirish.

$$n=-x-2-mx$$

m uchun yechish

$$\left\{\begin{matrix}m=-\frac{x+n+2}{x}\text{, }&x\neq 0\text{ and }x\neq 5\text{ and }x\neq 2\\m\in \mathrm{R}\text{, }&x=0\text{ and }n=-2\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini \left(x-5\right)\left(x-2\right) ga, x^{2}-7x+10,x-5 ning eng kichik karralisiga ko‘paytiring.

$$x^{2}+mx+n=\left(x-2\right)\left(x+1\right)$$

x-2 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+mx+n=x^{2}-x-2$$

Ikkala tarafdan x^{2} ni ayirish.

$$mx+n=x^{2}-x-2-x^{2}$$

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

$$mx+n=-x-2$$

Ikkala tarafdan n ni ayirish.

$$mx=-x-2-n$$

Tenglama standart shaklda.

$$xm=-x-n-2$$

Ikki tarafini x ga bo‘ling.

$$\frac{xm}{x}=\frac{-x-n-2}{x}$$

x ga bo'lish x ga ko'paytirishni bekor qiladi.

$$m=\frac{-x-n-2}{x}$$

-x-2-n ni x ga bo'lish.

$$m=-\frac{x+n+2}{x}$$

n uchun yechish

$$n=-\left(mx+x+2\right)$$

$$x\neq 5\text{ and }x\neq 2$$

Yechim qadamlari

Tenglamaning ikkala tarafini \left(x-5\right)\left(x-2\right) ga, x^{2}-7x+10,x-5 ning eng kichik karralisiga ko‘paytiring.

$$x^{2}+mx+n=\left(x-2\right)\left(x+1\right)$$

x-2 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+mx+n=x^{2}-x-2$$

Ikkala tarafdan x^{2} ni ayirish.

$$mx+n=x^{2}-x-2-x^{2}$$

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

$$mx+n=-x-2$$

Ikkala tarafdan mx ni ayirish.

$$n=-x-2-mx$$