left(1-kright)x^2+x+1-k=0 eching

$$\left( 1-k \right) { x }^{ 2 } +x+1-k = 0$$

k uchun yechish (complex solution)

$$k=\frac{x^{2}+x+1}{x^{2}+1}$$

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$x^{2}-kx^{2}+x+1-k=0$$

Ikkala tarafdan x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-kx^{2}+x+1-k=-x^{2}$$

Ikkala tarafdan x ni ayirish.

$$-kx^{2}+1-k=-x^{2}-x$$

Ikkala tarafdan 1 ni ayirish.

$$-kx^{2}-k=-x^{2}-x-1$$

k'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini -x^{2}-1 ga bo‘ling.

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

-x^{2}-1 ga bo'lish -x^{2}-1 ga ko'paytirishni bekor qiladi.

$$k=\frac{-x^{2}-x-1}{-x^{2}-1}$$

-x^{2}-x-1 ni -x^{2}-1 ga bo'lish.

$$k=\frac{x^{2}+x+1}{x^{2}+1}$$

k uchun yechish

$$k=\frac{x^{2}+x+1}{x^{2}+1}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$x^{2}-kx^{2}+x+1-k=0$$

Ikkala tarafdan x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-kx^{2}+x+1-k=-x^{2}$$

Ikkala tarafdan x ni ayirish.

$$-kx^{2}+1-k=-x^{2}-x$$

Ikkala tarafdan 1 ni ayirish.

$$-kx^{2}-k=-x^{2}-x-1$$

k'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini -x^{2}-1 ga bo‘ling.

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

-x^{2}-1 ga bo'lish -x^{2}-1 ga ko'paytirishni bekor qiladi.

$$k=\frac{-x^{2}-x-1}{-x^{2}-1}$$

-x^{2}-x-1 ni -x^{2}-1 ga bo'lish.

$$k=\frac{x^{2}+x+1}{x^{2}+1}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{\left(3-2k\right)\left(-2\left(1-k\right)+1\right)}-1}{2\left(1-k\right)}\text{; }x=\frac{\sqrt{-4k^{2}+8k-3}+1}{2\left(k-1\right)}\text{, }&k\neq 1\\x=0\text{, }&k=1\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{-\left(1-2k\right)\left(3-2k\right)}-1}{2\left(1-k\right)}\text{; }x=-\frac{\sqrt{-\left(1-2k\right)\left(3-2k\right)}+1}{2\left(1-k\right)}\text{, }&k\neq 1\text{ and }k\leq \frac{3}{2}\text{ and }k\geq \frac{1}{2}\\x=0\text{, }&k=1\end{matrix}\right,$$