x-sqrt{x^2-2x}=0 eching

$$x- \sqrt{ { x }^{ 2 } -2x } =0$$

x uchun yechish

$$x=0$$

Yechim qadamlari

Tenglamaning ikkala tarafidan x ni ayirish.

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

-1ni ikki tarafidan bekor qilish.

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

Tenglamaning ikkala taraf kvadratini chiqarish.

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

2 daraja ko‘rsatkichini \sqrt{x^{2}-2x} ga hisoblang va x^{2}-2x ni qiymatni oling.

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

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}-2x-x^{2}=0$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$-2x=0$$

Ikki son koʻpaytmasi 0 ga teng, agar kamida bittasi 0 bo‘lsa. -2 0 ga teng bo‘lmasa, x 0 ga teng bo‘lishi kerak.

$$x=0$$

x-\sqrt{x^{2}-2x}=0 tenglamasida x uchun 0 ni almashtiring.

$$0-\sqrt{0^{2}-2\times 0}=0$$

Qisqartirish. x=0 tenglamani qoniqtiradi.

$$0=0$$

\sqrt{x^{2}-2x}=x tenglamasi noyob yechimga ega.

$$x=0$$