3x+A^4/9+A^2=9-A^2 eching

$$3 x + \frac { A ^ { 4 } } { 9 + A ^ { 2 } } = 9 - A ^ { 2 }$$

x uchun yechish (complex solution)

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

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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.

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

Ikkala tarafdan A^{4} ni ayirish.

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

-2A^{4} ni olish uchun -A^{4} va -A^{4} ni birlashtirish.

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

x'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini 3A^{2}+27 ga bo‘ling.

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

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

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

81-2A^{4} ni 3A^{2}+27 ga bo'lish.

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

x uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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.

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

Ikkala tarafdan A^{4} ni ayirish.

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

-2A^{4} ni olish uchun -A^{4} va -A^{4} ni birlashtirish.

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

x'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini 3A^{2}+27 ga bo‘ling.

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

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

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

81-2A^{4} ni 3A^{2}+27 ga bo'lish.

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

A uchun yechish (complex solution)

$$A=\frac{\sqrt{3\sqrt{x^{2}-24x+72}-3x}}{2}$$

$$A=-\frac{\sqrt{3\sqrt{x^{2}-24x+72}-3x}}{2}$$

$$A=-\frac{\sqrt{-3\sqrt{x^{2}-24x+72}-3x}}{2}$$

$$A=\frac{\sqrt{-3\sqrt{x^{2}-24x+72}-3x}}{2}$$

A uchun yechish

$$A=-\frac{\sqrt{3\left(\sqrt{x^{2}-24x+72}-x\right)}}{2}$$

$$A=\frac{\sqrt{3\left(\sqrt{x^{2}-24x+72}-x\right)}}{2}\text{, }x\leq 3$$