x^2-2ax+1=0 eching

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

a uchun yechish

$$a=\frac{x}{2}+\frac{1}{2x}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

Ikkala tarafdan 1 ni ayirish.

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

Tenglama standart shaklda.

$$\left(-2x\right)a=-x^{2}-1$$

Ikki tarafini -2x ga bo‘ling.

$$\frac{\left(-2x\right)a}{-2x}=\frac{-x^{2}-1}{-2x}$$

-2x ga bo'lish -2x ga ko'paytirishni bekor qiladi.

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

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

$$a=\frac{x}{2}+\frac{1}{2x}$$

x uchun yechish (complex solution)

$$x=\sqrt{a^{2}-1}+a$$

$$x=-\sqrt{a^{2}-1}+a$$

x uchun yechish

$$x=\sqrt{a^{2}-1}+a$$

$$x=-\sqrt{a^{2}-1}+a\text{, }|a|\geq 1$$