x^2-4kx+k+3=0 eching

$$x ^ { 2 } - 4 k x + k + 3 = 0$$

k uchun yechish

$$k=-\frac{x^{2}+3}{1-4x}$$

$$x\neq \frac{1}{4}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$-4kx+k+3=-x^{2}$$

Ikkala tarafdan 3 ni ayirish.

$$-4kx+k=-x^{2}-3$$

k'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-4x+1\right)k=-x^{2}-3$$

Tenglama standart shaklda.

$$\left(1-4x\right)k=-x^{2}-3$$

Ikki tarafini -4x+1 ga bo‘ling.

$$\frac{\left(1-4x\right)k}{1-4x}=\frac{-x^{2}-3}{1-4x}$$

-4x+1 ga bo'lish -4x+1 ga ko'paytirishni bekor qiladi.

$$k=\frac{-x^{2}-3}{1-4x}$$

-x^{2}-3 ni -4x+1 ga bo'lish.

$$k=-\frac{x^{2}+3}{1-4x}$$

x uchun yechish (complex solution)

$$x=\sqrt{\left(k-1\right)\left(4k+3\right)}+2k$$

$$x=-\sqrt{\left(k-1\right)\left(4k+3\right)}+2k$$

x uchun yechish

$$x=\sqrt{\left(k-1\right)\left(4k+3\right)}+2k$$

$$x=-\sqrt{\left(k-1\right)\left(4k+3\right)}+2k\text{, }k\leq -\frac{3}{4}\text{ or }k\geq 1$$