18x=0x+36sqrt{1-x^2} eching

$$18 x = 0 x + 36 \sqrt { 1 - x ^ { 2 } }$$

x uchun yechish

$$x=\frac{2\sqrt{5}}{5}\approx 0,894427191$$

Yechim qadamlari

Tenglamaning ikkala tarafidan 0 ni ayirish.

$$18x=36\sqrt{1-x^{2}}$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$18x+0=36\sqrt{1-x^{2}}$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$18x=36\sqrt{1-x^{2}}$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(18x\right)^{2}=\left(36\sqrt{1-x^{2}}\right)^{2}$$

\left(18x\right)^{2} ni kengaytirish.

$$18^{2}x^{2}=\left(36\sqrt{1-x^{2}}\right)^{2}$$

2 daraja ko‘rsatkichini 18 ga hisoblang va 324 ni qiymatni oling.

$$324x^{2}=\left(36\sqrt{1-x^{2}}\right)^{2}$$

\left(36\sqrt{1-x^{2}}\right)^{2} ni kengaytirish.

$$324x^{2}=36^{2}\left(\sqrt{1-x^{2}}\right)^{2}$$

2 daraja ko‘rsatkichini 36 ga hisoblang va 1296 ni qiymatni oling.

$$324x^{2}=1296\left(\sqrt{1-x^{2}}\right)^{2}$$

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

$$324x^{2}=1296\left(1-x^{2}\right)$$

1296 ga 1-x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$324x^{2}=1296-1296x^{2}$$

1296x^{2} ni ikki tarafga qo’shing.

$$324x^{2}+1296x^{2}=1296$$

1620x^{2} ni olish uchun 324x^{2} va 1296x^{2} ni birlashtirish.

$$1620x^{2}=1296$$

Ikki tarafini 1620 ga bo‘ling.

$$x^{2}=\frac{1296}{1620}$$

\frac{1296}{1620} ulushini 324 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{4}{5}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{2\sqrt{5}}{5} x=-\frac{2\sqrt{5}}{5}$$

18x=0x+36\sqrt{1-x^{2}} tenglamasida x uchun \frac{2\sqrt{5}}{5} ni almashtiring.

$$18\times \frac{2\sqrt{5}}{5}=0\times \frac{2\sqrt{5}}{5}+36\sqrt{1-\left(\frac{2\sqrt{5}}{5}\right)^{2}}$$

Qisqartirish. x=\frac{2\sqrt{5}}{5} tenglamani qoniqtiradi.

$$\frac{36}{5}\times 5^{\frac{1}{2}}=\frac{36}{5}\times 5^{\frac{1}{2}}$$

18x=0x+36\sqrt{1-x^{2}} tenglamasida x uchun -\frac{2\sqrt{5}}{5} ni almashtiring.

$$18\left(-\frac{2\sqrt{5}}{5}\right)=0\left(-\frac{2\sqrt{5}}{5}\right)+36\sqrt{1-\left(-\frac{2\sqrt{5}}{5}\right)^{2}}$$

Qisqartirish. x=-\frac{2\sqrt{5}}{5} qiymati bu tenglamani qoniqtirmaydi, chunki oʻng va chap tarafdagi belgilar bir-biriga qarama-qarshi.

$$-\frac{36}{5}\times 5^{\frac{1}{2}}=\frac{36}{5}\times 5^{\frac{1}{2}}$$

18x=36\sqrt{1-x^{2}} tenglamasi noyob yechimga ega.

$$x=\frac{2\sqrt{5}}{5}$$