x=sqrt{x+x^2} eching

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

x uchun yechish

$$x=0$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

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

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

$$x^{2}=x+x^{2}$$

Ikkala tarafdan x ni ayirish.

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

Ikkala tarafdan x^{2} ni ayirish.

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

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

$$-x=0$$

Ikki son koʻpaytmasi 0 ga teng, agar kamida bittasi 0 bo‘lsa. -1 0 ga teng bo‘lmasa, x 0 ga teng bo‘lishi kerak.

$$x=0$$

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

$$0=\sqrt{0+0^{2}}$$

Qisqartirish. x=0 tenglamani qoniqtiradi.

$$0=0$$

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

$$x=0$$