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

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

Réitigh do s.

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

$$x\neq 0$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Iolraigh an dá thaobh den chothromóid faoi 12, an comhiolraí is lú de 3,4,6.

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

Méadaigh x agus x chun x^{2} a fháil.

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

Méadaigh 4 agus 3 chun 12 a fháil.

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

Méadaigh 3 agus 4 chun 12 a fháil.

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

Comhcheangail 12x agus 12x chun 24x a fháil.

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

Méadaigh 12 agus 2 chun 24 a fháil.

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

Úsáid an t-airí dáileach chun 24 a mhéadú faoi \frac{x}{4}-8.

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

Cealaigh an comhfhachtóir 4 is mó in 24 agus 4.

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

Comhcheangail 24x agus 6x chun 30x a fháil.

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

Bain 30x ón dá thaobh.

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

Cuir 192 leis an dá thaobh.

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

Suimigh 6048 agus 192 chun 6240 a fháil.

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

Roinn an dá thaobh faoi 2x^{2}.

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

Má roinntear é faoi 2x^{2} cuirtear an iolrúchán faoi 2x^{2} ar ceal.

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

Roinn 6240-30x faoi 2x^{2}.

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

Réitigh do x. (complex solution)

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

Réitigh do x.

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