y=frac{sqrt{-x^2}}{x} eching

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

x uchun yechish

$$x\neq 0$$

$$\left(arg(-ix)<\pi \text{ and }x\neq 0\text{ and }y=-i\right)\text{ or }\left(arg(ix)<\pi \text{ and }x\neq 0\text{ and }y=i\right)$$

Yechim qadamlari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

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

Ikkala tarafdan \sqrt{-x^{2}} ni ayirish.

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

Tenglamaning ikkala tarafidan yx ni ayirish.

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

-1ni ikki tarafidan bekor qilish.

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

Tenglamaning ikkala taraf kvadratini chiqarish.

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

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

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

\left(yx\right)^{2} ni kengaytirish.

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

Ikkala tarafdan y^{2}x^{2} ni ayirish.

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

Shartlarni qayta saralash.

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

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-y^{2}-1\right)x^{2}=0$$

-y^{2}-1 ga bo'lish -y^{2}-1 ga ko'paytirishni bekor qiladi.

$$x^{2}=\frac{0}{-y^{2}-1}$$

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

$$x^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=0 x=0$$

Tenglama yechildi. Yechimlar bir xil.

$$x=0$$

y=\frac{\sqrt{-x^{2}}}{x} tenglamasida x uchun 0 ni almashtiring. Bu ifoda noaniq.

$$y=\frac{\sqrt{-0^{2}}}{0}$$

\sqrt{-x^{2}}=xy tenglamasining yechimlari mavjud emas.

$$x\in \emptyset$$

y uchun yechish

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

$$x\neq 0$$