3x-A(A^3/9+A^2)=9-A^2 eching

$$3 x - A ( \frac { A ^ { 3 } } { 9 + A ^ { 2 } } ) = 9 - A ^ { 2 }$$

x uchun yechish (complex solution)

$$x=\frac{27}{A^{2}+9}$$

$$A\neq -3i\text{ and }A\neq 3i$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini \left(A-3i\right)\left(A+3i\right) ga ko'paytirish.

$$3x\left(A-3i\right)\left(A+3i\right)-AA^{3}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 3 ni qo‘shib, 4 ni oling.

$$3x\left(A-3i\right)\left(A+3i\right)-A^{4}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

3x ga A-3i ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(3xA-9ix\right)\left(A+3i\right)-A^{4}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

3xA-9ix ga A+3i ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3xA^{2}+27x-A^{4}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

A-3i ga A+3i ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3xA^{2}+27x-A^{4}=\left(A^{2}+9\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)$$

A^{2}+9 ga 9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xA^{2}+27x-A^{4}=9A^{2}+81-A^{2}\left(A-3i\right)\left(A+3i\right)$$

-A^{2} ga A-3i ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xA^{2}+27x-A^{4}=9A^{2}+81+\left(-A^{3}+3iA^{2}\right)\left(A+3i\right)$$

-A^{3}+3iA^{2} ga A+3i ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3xA^{2}+27x-A^{4}=9A^{2}+81-A^{4}-9A^{2}$$

0 ni olish uchun 9A^{2} va -9A^{2} ni birlashtirish.

$$3xA^{2}+27x-A^{4}=81-A^{4}$$

A^{4} ni ikki tarafga qo’shing.

$$3xA^{2}+27x=81-A^{4}+A^{4}$$

0 ni olish uchun -A^{4} va A^{4} ni birlashtirish.

$$3xA^{2}+27x=81$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(3A^{2}+27\right)x=81$$

Ikki tarafini 3A^{2}+27 ga bo‘ling.

$$\frac{\left(3A^{2}+27\right)x}{3A^{2}+27}=\frac{81}{3A^{2}+27}$$

3A^{2}+27 ga bo'lish 3A^{2}+27 ga ko'paytirishni bekor qiladi.

$$x=\frac{81}{3A^{2}+27}$$

81 ni 3A^{2}+27 ga bo'lish.

$$x=\frac{27}{A^{2}+9}$$

x uchun yechish

$$x=\frac{27}{A^{2}+9}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini A^{2}+9 ga ko'paytirish.

$$3x\left(A^{2}+9\right)-AA^{3}=\left(A^{2}+9\right)\times 9-A^{2}\left(A^{2}+9\right)$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 3 ni qo‘shib, 4 ni oling.

$$3x\left(A^{2}+9\right)-A^{4}=\left(A^{2}+9\right)\times 9-A^{2}\left(A^{2}+9\right)$$

3x ga A^{2}+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xA^{2}+27x-A^{4}=\left(A^{2}+9\right)\times 9-A^{2}\left(A^{2}+9\right)$$

A^{2}+9 ga 9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xA^{2}+27x-A^{4}=9A^{2}+81-A^{2}\left(A^{2}+9\right)$$

-A^{2} ga A^{2}+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3xA^{2}+27x-A^{4}=9A^{2}+81-A^{4}-9A^{2}$$

0 ni olish uchun 9A^{2} va -9A^{2} ni birlashtirish.

$$3xA^{2}+27x-A^{4}=81-A^{4}$$

A^{4} ni ikki tarafga qo’shing.

$$3xA^{2}+27x=81-A^{4}+A^{4}$$

0 ni olish uchun -A^{4} va A^{4} ni birlashtirish.

$$3xA^{2}+27x=81$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(3A^{2}+27\right)x=81$$

Ikki tarafini 3A^{2}+27 ga bo‘ling.

$$\frac{\left(3A^{2}+27\right)x}{3A^{2}+27}=\frac{81}{3A^{2}+27}$$

3A^{2}+27 ga bo'lish 3A^{2}+27 ga ko'paytirishni bekor qiladi.

$$x=\frac{81}{3A^{2}+27}$$

81 ni 3A^{2}+27 ga bo'lish.

$$x=\frac{27}{A^{2}+9}$$

A uchun yechish (complex solution)

$$A=-3\sqrt{-1+\frac{3}{x}}$$

$$A=3\sqrt{-1+\frac{3}{x}}\text{, }x\neq 0$$

A uchun yechish

$$A=3\sqrt{-1+\frac{3}{x}}$$

$$A=-3\sqrt{-1+\frac{3}{x}}\text{, }x>0\text{ and }x\leq 3$$