2x^2+kx-1=0 eching

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

k uchun yechish

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

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

1 ni ikki tarafga qo’shing.

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

Tenglama standart shaklda.

$$xk=1-2x^{2}$$

Ikki tarafini x ga bo‘ling.

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

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

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

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

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

x uchun yechish

$$x=\frac{\sqrt{k^{2}+8}-k}{4}$$

$$x=\frac{-\sqrt{k^{2}+8}-k}{4}$$