y^2(a+x)=x^2(3a-x) eching

$$y ^ { 2 } ( a + x ) = x ^ { 2 } ( 3 a - x )$$

a uchun yechish

$$\left\{\begin{matrix}a=-\frac{x\left(x^{2}+y^{2}\right)}{y^{2}-3x^{2}}\text{, }&|y|\neq \sqrt{3}|x|\\a\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y^{2} ga a+x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}a+y^{2}x=x^{2}\left(3a-x\right)$$

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

$$y^{2}a+y^{2}x=3x^{2}a-x^{3}$$

Ikkala tarafdan 3x^{2}a ni ayirish.

$$y^{2}a+y^{2}x-3x^{2}a=-x^{3}$$

Ikkala tarafdan y^{2}x ni ayirish.

$$y^{2}a-3x^{2}a=-x^{3}-y^{2}x$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(y^{2}-3x^{2}\right)a=-x^{3}-y^{2}x$$

Tenglama standart shaklda.

$$\left(y^{2}-3x^{2}\right)a=-x^{3}-xy^{2}$$

Ikki tarafini y^{2}-3x^{2} ga bo‘ling.

$$\frac{\left(y^{2}-3x^{2}\right)a}{y^{2}-3x^{2}}=-\frac{x\left(x^{2}+y^{2}\right)}{y^{2}-3x^{2}}$$

y^{2}-3x^{2} ga bo'lish y^{2}-3x^{2} ga ko'paytirishni bekor qiladi.

$$a=-\frac{x\left(x^{2}+y^{2}\right)}{y^{2}-3x^{2}}$$