x/3*3+x/4*4+x/6*xs+(x/4-8)*2=504 eching

$$\frac { x } { 3 } \times 3 + \frac { x } { 4 } \times 4 + \frac { x } { 6 } \cdot x s + ( \frac { x } { 4 } - 8 ) \cdot 2 = 504$$

s uchun yechish

$$s=-\frac{15\left(x-208\right)}{x^{2}}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 12 ga, 3,4,6 ning eng kichik karralisiga ko‘paytiring.

$$4x\times 3+3x\times 4+2xxs+12\left(\frac{x}{4}-8\right)\times 2=6048$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$4x\times 3+3x\times 4+2x^{2}s+12\left(\frac{x}{4}-8\right)\times 2=6048$$

12 hosil qilish uchun 4 va 3 ni ko'paytirish.

$$12x+3x\times 4+2x^{2}s+12\left(\frac{x}{4}-8\right)\times 2=6048$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$12x+12x+2x^{2}s+12\left(\frac{x}{4}-8\right)\times 2=6048$$

24x ni olish uchun 12x va 12x ni birlashtirish.

$$24x+2x^{2}s+12\left(\frac{x}{4}-8\right)\times 2=6048$$

24 hosil qilish uchun 12 va 2 ni ko'paytirish.

$$24x+2x^{2}s+24\left(\frac{x}{4}-8\right)=6048$$

24 ga \frac{x}{4}-8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$24x+2x^{2}s+24\times \frac{x}{4}-192=6048$$

24 va 4 ichida eng katta umumiy 4 faktorini bekor qiling.

$$24x+2x^{2}s+6x-192=6048$$

30x ni olish uchun 24x va 6x ni birlashtirish.

$$30x+2x^{2}s-192=6048$$

Ikkala tarafdan 30x ni ayirish.

$$2x^{2}s-192=6048-30x$$

192 ni ikki tarafga qo’shing.

$$2x^{2}s=6048-30x+192$$

6240 olish uchun 6048 va 192'ni qo'shing.

$$2x^{2}s=6240-30x$$

Ikki tarafini 2x^{2} ga bo‘ling.

$$\frac{2x^{2}s}{2x^{2}}=\frac{6240-30x}{2x^{2}}$$

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

$$s=\frac{6240-30x}{2x^{2}}$$

6240-30x ni 2x^{2} ga bo'lish.

$$s=\frac{15\left(208-x\right)}{x^{2}}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{15\left(832s+15\right)}-15}{2s}\text{; }x=-\frac{\sqrt{15}\left(\sqrt{832s+15}+\sqrt{15}\right)}{2s}\text{, }&s\neq 0\\x=208\text{, }&s=0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{15\left(832s+15\right)}-15}{2s}\text{; }x=-\frac{\sqrt{15}\left(\sqrt{832s+15}+\sqrt{15}\right)}{2s}\text{, }&s\neq 0\text{ and }s\geq -\frac{15}{832}\\x=208\text{, }&s=0\end{matrix}\right,$$