Réitigh (x+2)*(y-6)^2=81

$$( x + 2 ) \cdot ( y - 6 ) ^ { 2 } = 81$$

Réitigh do x.

$$x=-\frac{2y^{2}-24y-9}{\left(y-6\right)^{2}}$$

$$y\neq 6$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(y-6\right)^{2} a leathnú.

$$\left(x+2\right)\left(y^{2}-12y+36\right)=81$$

Úsáid an t-airí dáileach chun x+2 a mhéadú faoi y^{2}-12y+36.

$$xy^{2}-12xy+36x+2y^{2}-24y+72=81$$

Bain 2y^{2} ón dá thaobh.

$$xy^{2}-12xy+36x-24y+72=81-2y^{2}$$

Cuir 24y leis an dá thaobh.

$$xy^{2}-12xy+36x+72=81-2y^{2}+24y$$

Bain 72 ón dá thaobh.

$$xy^{2}-12xy+36x=81-2y^{2}+24y-72$$

Dealaigh 72 ó 81 chun 9 a fháil.

$$xy^{2}-12xy+36x=9-2y^{2}+24y$$

Comhcheangail na téarmaí ar fad ina bhfuil x.

$$\left(y^{2}-12y+36\right)x=9-2y^{2}+24y$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(y^{2}-12y+36\right)x=9+24y-2y^{2}$$

Roinn an dá thaobh faoi y^{2}-12y+36.

$$\frac{\left(y^{2}-12y+36\right)x}{y^{2}-12y+36}=\frac{9+24y-2y^{2}}{y^{2}-12y+36}$$

Má roinntear é faoi y^{2}-12y+36 cuirtear an iolrúchán faoi y^{2}-12y+36 ar ceal.

$$x=\frac{9+24y-2y^{2}}{y^{2}-12y+36}$$

Roinn 9-2y^{2}+24y faoi y^{2}-12y+36.

$$x=\frac{9+24y-2y^{2}}{\left(y-6\right)^{2}}$$

Réitigh do y. (complex solution)

$$y=6+9\left(x+2\right)^{-\frac{1}{2}}$$

$$y=6-9\left(x+2\right)^{-\frac{1}{2}}\text{, }x\neq -2$$

Réitigh do y.

$$y=6+\frac{9}{\sqrt{x+2}}$$

$$y=6-\frac{9}{\sqrt{x+2}}\text{, }x>-2$$