3x^2-ksqrt{3}x+4=0 eching

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

k uchun yechish

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

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 4 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

Ikkala tarafdan 3x^{2} ni ayirish.

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

Tenglama standart shaklda.

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

Ikki tarafini -\sqrt{3}x ga bo‘ling.

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

-\sqrt{3}x ga bo'lish -\sqrt{3}x ga ko'paytirishni bekor qiladi.

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

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

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

x uchun yechish (complex solution)

$$x=\frac{\sqrt{3}\left(\sqrt{k^{2}-16}+k\right)}{6}$$

$$x=-\frac{\sqrt{3}\left(\sqrt{k^{2}-16}-k\right)}{6}$$

x uchun yechish

$$x=-\frac{\sqrt{3}\left(\sqrt{k^{2}-16}-k\right)}{6}$$

$$x=\frac{\sqrt{3}\left(\sqrt{k^{2}-16}+k\right)}{6}\text{, }|k|\geq 4$$