x=sqrt{x}*x+x/x eching

$$x = \sqrt { x } \times \frac { x + x } { x }$$

x uchun yechish

$$x=4$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

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

2x ni olish uchun x va x ni birlashtirish.

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

Surat va maxrajdagi ikkala x ni qisqartiring.

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

\left(\sqrt{x}\times 2\right)^{2} ni kengaytirish.

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

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

$$x^{2}=x\times 2^{2}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$x^{2}=x\times 4$$

Ikkala tarafdan x\times 4 ni ayirish.

$$x^{2}-x\times 4=0$$

-4 hosil qilish uchun -1 va 4 ni ko'paytirish.

$$x^{2}-4x=0$$

x omili.

$$x\left(x-4\right)=0$$

Tenglamani yechish uchun x=0 va x-4=0 ni yeching.

$$x=0 x=4$$

x=\sqrt{x}\times \frac{x+x}{x} tenglamasida x uchun 0 ni almashtiring. Bu ifoda noaniq.

$$0=\sqrt{0}\times \frac{0+0}{0}$$

x=\sqrt{x}\times \frac{x+x}{x} tenglamasida x uchun 4 ni almashtiring.

$$4=\sqrt{4}\times \frac{4+4}{4}$$

Qisqartirish. x=4 tenglamani qoniqtiradi.

$$4=4$$

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

$$x=4$$