x^2+2sqrt{2}kx+18=0 eching

$${ x }^{ 2 } +2 \sqrt{ 2 } kx+18=0$$

k uchun yechish

$$k=-\frac{\sqrt{2}\left(x^{2}+18\right)}{4x}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2\sqrt{2}kx+18=-x^{2}$$

Ikkala tarafdan 18 ni ayirish.

$$2\sqrt{2}kx=-x^{2}-18$$

Tenglama standart shaklda.

$$2\sqrt{2}xk=-x^{2}-18$$

Ikki tarafini 2\sqrt{2}x ga bo‘ling.

$$\frac{2\sqrt{2}xk}{2\sqrt{2}x}=\frac{-x^{2}-18}{2\sqrt{2}x}$$

2\sqrt{2}x ga bo'lish 2\sqrt{2}x ga ko'paytirishni bekor qiladi.

$$k=\frac{-x^{2}-18}{2\sqrt{2}x}$$

-x^{2}-18 ni 2\sqrt{2}x ga bo'lish.

$$k=-\frac{\sqrt{2}\left(x^{2}+18\right)}{4x}$$

x uchun yechish (complex solution)

$$x=\sqrt{2}\left(\sqrt{k^{2}-9}-k\right)$$

$$x=\sqrt{2}\left(-\sqrt{k^{2}-9}-k\right)$$

x uchun yechish

$$x=\sqrt{2}\left(\sqrt{k^{2}-9}-k\right)$$

$$x=\sqrt{2}\left(-\sqrt{k^{2}-9}-k\right)\text{, }|k|\geq 3$$