x^2+2x=k(x-1) eching

$$x ^ { 2 } + 2 x = k ( x - 1 )$$

k uchun yechish

$$k=-\frac{x\left(x+2\right)}{1-x}$$

$$x\neq 1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

k ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+2x=kx-k$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$kx-k=x^{2}+2x$$

k'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini x-1 ga bo‘ling.

$$\frac{\left(x-1\right)k}{x-1}=\frac{x\left(x+2\right)}{x-1}$$

x-1 ga bo'lish x-1 ga ko'paytirishni bekor qiladi.

$$k=\frac{x\left(x+2\right)}{x-1}$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{k^{2}-8k+4}+k-2}{2}$$

$$x=\frac{-\sqrt{k^{2}-8k+4}+k-2}{2}$$

x uchun yechish

$$x=\frac{\sqrt{k^{2}-8k+4}+k-2}{2}$$

$$x=\frac{-\sqrt{k^{2}-8k+4}+k-2}{2}\text{, }k\geq 2\sqrt{3}+4\text{ or }k\leq 4-2\sqrt{3}$$