Whakaoti i te {l}{(x-y)(x+y)=x^2-(y-1)^2}{(x+y)(x+2)-xy=x^2}

$$\left\{ \begin{array} { l } { ( x - y ) ( x + y ) = x ^ { 2 } - ( y - 1 ) ^ { 2 } } \\ { ( x + y ) ( x + 2 ) - x y = x ^ { 2 } } \end{array} \right.$$

Whakaoti mō x, y

$$x=-\frac{1}{2}=-0.5$$

$$y=\frac{1}{2}=0.5$$

Ngā Upane Otinga

Whakaarohia te whārite tuatahi. Whakaarohia te \left(x-y\right)\left(x+y\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x^{2}-y^{2}=x^{2}-\left(y-1\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(y-1\right)^{2}.

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

Hei kimi i te tauaro o y^{2}-2y+1, kimihia te tauaro o ia taurangi.

$$x^{2}-y^{2}=x^{2}-y^{2}+2y-1$$

Tangohia te x^{2} mai i ngā taha e rua.

$$x^{2}-y^{2}-x^{2}=-y^{2}+2y-1$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$-y^{2}=-y^{2}+2y-1$$

Me tāpiri te y^{2} ki ngā taha e rua.

$$-y^{2}+y^{2}=2y-1$$

Pahekotia te -y^{2} me y^{2}, ka 0.

$$0=2y-1$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2y-1=0$$

Me tāpiri te 1 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$2y=1$$

Whakawehea ngā taha e rua ki te 2.

$$y=\frac{1}{2}$$

Whakaarohia te whārite tuarua. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te x+\frac{1}{2} ki te x+2 ka whakakotahi i ngā kupu rite.

$$x^{2}+\frac{5}{2}x+1-x\times \frac{1}{2}=x^{2}$$

Whakareatia te -1 ki te \frac{1}{2}, ka -\frac{1}{2}.

$$x^{2}+\frac{5}{2}x+1-\frac{1}{2}x=x^{2}$$

Pahekotia te \frac{5}{2}x me -\frac{1}{2}x, ka 2x.

$$x^{2}+2x+1=x^{2}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$x^{2}+2x+1-x^{2}=0$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$2x+1=0$$

Tangohia te 1 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$2x=-1$$

Whakawehea ngā taha e rua ki te 2.

$$x=-\frac{1}{2}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{1}{2} y=\frac{1}{2}$$