left(k-2right)x^2-x-4k=0 eching

$$\left( k-2 \right) { x }^{ 2 } -x-4k=0$$

k uchun yechish (complex solution)

$$k=\frac{x\left(2x+1\right)}{x^{2}-4}$$

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

k-2 ga x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx^{2}-2x^{2}-x-4k=0$$

2x^{2} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$kx^{2}-x-4k=2x^{2}$$

x ni ikki tarafga qo’shing.

$$kx^{2}-4k=2x^{2}+x$$

k'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-4\right)k=2x^{2}+x$$

Ikki tarafini x^{2}-4 ga bo‘ling.

$$\frac{\left(x^{2}-4\right)k}{x^{2}-4}=\frac{x\left(2x+1\right)}{x^{2}-4}$$

x^{2}-4 ga bo'lish x^{2}-4 ga ko'paytirishni bekor qiladi.

$$k=\frac{x\left(2x+1\right)}{x^{2}-4}$$

k uchun yechish

$$k=\frac{x\left(2x+1\right)}{x^{2}-4}$$

$$|x|\neq 2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

k-2 ga x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx^{2}-2x^{2}-x-4k=0$$

2x^{2} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$kx^{2}-x-4k=2x^{2}$$

x ni ikki tarafga qo’shing.

$$kx^{2}-4k=2x^{2}+x$$

k'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-4\right)k=2x^{2}+x$$

Ikki tarafini x^{2}-4 ga bo‘ling.

$$\frac{\left(x^{2}-4\right)k}{x^{2}-4}=\frac{x\left(2x+1\right)}{x^{2}-4}$$

x^{2}-4 ga bo'lish x^{2}-4 ga ko'paytirishni bekor qiladi.

$$k=\frac{x\left(2x+1\right)}{x^{2}-4}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{16k^{2}-32k+1}+1}{2\left(k-2\right)}\text{; }x=\frac{-\sqrt{16k^{2}-32k+1}+1}{2\left(k-2\right)}\text{, }&k\neq 2\\x=-8\text{, }&k=2\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{16k^{2}-32k+1}+1}{2\left(k-2\right)}\text{; }x=\frac{-\sqrt{16k^{2}-32k+1}+1}{2\left(k-2\right)}\text{, }&k\leq -\frac{\sqrt{15}}{4}+1\text{ or }\left(k\neq 2\text{ and }k\geq \frac{\sqrt{15}}{4}+1\right)\\x=-8\text{, }&k=2\end{matrix}\right,$$