Whakaoti i te (y-1)^2+2y(1-y)=0

$$( y - 1 ) ^ { 2 } + 2 y ( 1 - y ) = 0$$

Whakaoti mō y

$$y=1$$

$$y=-1$$

Ngā Upane mā te Kimi Pūtakerua

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

$$y^{2}-2y+1+2y\left(1-y\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2y ki te 1-y.

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

Pahekotia te -2y me 2y, ka 0.

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

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

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

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

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

Whakawehea ngā taha e rua ki te -1.

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

Whakawehea te -1 ki te -1, kia riro ko 1.

$$y^{2}=1$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$y=1 y=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$y^{2}-2y+1+2y\left(1-y\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2y ki te 1-y.

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

Pahekotia te -2y me 2y, ka 0.

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

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

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 0 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-1\right)}}{2\left(-1\right)}$$

Pūrua 0.

$$y=\frac{0±\sqrt{-4\left(-1\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$y=\frac{0±\sqrt{4}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 4.

$$y=\frac{0±2}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$y=\frac{0±2}{-2}$$

Nā, me whakaoti te whārite y=\frac{0±2}{-2} ina he tāpiri te ±. Whakawehe 2 ki te -2.

$$y=-1$$

Nā, me whakaoti te whārite y=\frac{0±2}{-2} ina he tango te ±. Whakawehe -2 ki te -2.

$$y=1$$

Kua oti te whārite te whakatau.

$$y=-1 y=1$$