4x^2-3kx+1=0 eching

$$4 x ^ { 2 } - 3 k x + 1 = 0$$

k uchun yechish

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

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 4x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-3kx+1=-4x^{2}$$

Ikkala tarafdan 1 ni ayirish.

$$-3kx=-4x^{2}-1$$

Tenglama standart shaklda.

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

Ikki tarafini -3x ga bo‘ling.

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

-3x ga bo'lish -3x ga ko'paytirishni bekor qiladi.

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

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

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

x uchun yechish (complex solution)

$$x=\frac{\sqrt{9k^{2}-16}+3k}{8}$$

$$x=\frac{-\sqrt{9k^{2}-16}+3k}{8}$$

x uchun yechish

$$x=\frac{\sqrt{9k^{2}-16}+3k}{8}$$

$$x=\frac{-\sqrt{9k^{2}-16}+3k}{8}\text{, }|k|\geq \frac{4}{3}$$