4x=1-sqrt{1-x^2} eching

$$4 x = 1 - \sqrt { 1 - x ^ { 2 } }$$

x uchun yechish

$$x=0$$

Yechim qadamlari

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$4x-1=-\sqrt{1-x^{2}}$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(4x-1\right)^{2}=\left(-\sqrt{1-x^{2}}\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(4x-1\right)^{2} kengaytirilishi uchun ishlating.

$$16x^{2}-8x+1=\left(-\sqrt{1-x^{2}}\right)^{2}$$

\left(-\sqrt{1-x^{2}}\right)^{2} ni kengaytirish.

$$16x^{2}-8x+1=\left(-1\right)^{2}\left(\sqrt{1-x^{2}}\right)^{2}$$

2 daraja ko‘rsatkichini -1 ga hisoblang va 1 ni qiymatni oling.

$$16x^{2}-8x+1=1\left(\sqrt{1-x^{2}}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{1-x^{2}} ga hisoblang va 1-x^{2} ni qiymatni oling.

$$16x^{2}-8x+1=1\left(1-x^{2}\right)$$

1 ga 1-x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16x^{2}-8x+1=1-x^{2}$$

Ikkala tarafdan 1 ni ayirish.

$$16x^{2}-8x+1-1=-x^{2}$$

0 olish uchun 1 dan 1 ni ayirish.

$$16x^{2}-8x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$16x^{2}-8x+x^{2}=0$$

17x^{2} ni olish uchun 16x^{2} va x^{2} ni birlashtirish.

$$17x^{2}-8x=0$$

x omili.

$$x\left(17x-8\right)=0$$

Tenglamani yechish uchun x=0 va 17x-8=0 ni yeching.

$$x=0 x=\frac{8}{17}$$

4x=1-\sqrt{1-x^{2}} tenglamasida x uchun 0 ni almashtiring.

$$4\times 0=1-\sqrt{1-0^{2}}$$

Qisqartirish. x=0 tenglamani qoniqtiradi.

$$0=0$$

4x=1-\sqrt{1-x^{2}} tenglamasida x uchun \frac{8}{17} ni almashtiring.

$$4\times \frac{8}{17}=1-\sqrt{1-\left(\frac{8}{17}\right)^{2}}$$

Qisqartirish. x=\frac{8}{17} qiymati bu tenglamani qoniqtirmaydi.

$$\frac{32}{17}=\frac{2}{17}$$

4x-1=-\sqrt{1-x^{2}} tenglamasi noyob yechimga ega.

$$x=0$$