Réitigh alpha^2-0.8alpha+3.125beta=0

$$\alpha ^ { 2 } - 0.8 \alpha + 3.125 \beta = 0$$

Réitigh do β.

$$\beta =-\frac{8\alpha \left(\alpha -0.8\right)}{25}$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Bain \alpha ^{2} ón dá thaobh. Is ionann rud ar bith a dhealaítear ó nialas agus a shéanadh.

$$-0.8\alpha +3.125\beta =-\alpha ^{2}$$

Cuir 0.8\alpha leis an dá thaobh.

$$3.125\beta =-\alpha ^{2}+0.8\alpha$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$3.125\beta =-\alpha ^{2}+\frac{4\alpha }{5}$$

Roinn an dá thaobh den chothromóid faoi 3.125, arb ionann é sin agus an dá thaobh a mhéadú faoi dheilín an chodáin.

$$\frac{3.125\beta }{3.125}=\frac{\alpha \left(0.8-\alpha \right)}{3.125}$$

Má roinntear é faoi 3.125 cuirtear an iolrúchán faoi 3.125 ar ceal.

$$\beta =\frac{\alpha \left(0.8-\alpha \right)}{3.125}$$

Roinn \alpha \left(0.8-\alpha \right) faoi 3.125 trí \alpha \left(0.8-\alpha \right) a mhéadú faoi dheilín 3.125.

$$\beta =\frac{8\alpha \left(0.8-\alpha \right)}{25}$$

Réitigh do α. (complex solution)

$$\alpha =\frac{\sqrt{-\frac{25\beta }{2}+0.64}}{2}+0.4$$

$$\alpha =-\frac{\sqrt{-\frac{25\beta }{2}+0.64}}{2}+0.4$$

Réitigh do α.

$$\alpha =\frac{\sqrt{-\frac{25\beta }{2}+0.64}}{2}+0.4$$

$$\alpha =-\frac{\sqrt{-\frac{25\beta }{2}+0.64}}{2}+0.4\text{, }\beta \leq 0.0512$$