Whakaoti i te y^2-y=0

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

Whakaoti mō y

$$y=1$$

$$y=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te y.

$$y\left(y-1\right)=0$$

Hei kimi otinga whārite, me whakaoti te y=0 me te y-1=0.

$$y=0 y=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

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

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

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

Tuhia te pūtakerua o te 1.

$$y=\frac{-\left(-1\right)±1}{2}$$

Ko te tauaro o -1 ko 1.

$$y=\frac{1±1}{2}$$

Nā, me whakaoti te whārite y=\frac{1±1}{2} ina he tāpiri te ±. Tāpiri 1 ki te 1.

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

Whakawehe 2 ki te 2.

$$y=1$$

Nā, me whakaoti te whārite y=\frac{1±1}{2} ina he tango te ±. Tango 1 mai i 1.

$$y=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$y=0$$

Kua oti te whārite te whakatau.

$$y=1 y=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

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

Whakawehea te -1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{2}. Nā, tāpiria te pūrua o te -\frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$y^{2}-y+\frac{1}{4}=\frac{1}{4}$$

Tauwehea y^{2}-y+\frac{1}{4}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

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

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

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

Whakarūnātia.

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

Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.

$$y=1 y=0$$