Whakaoti i te 6u^2-24u=0

$$6 u ^ { 2 } - 24 u = 0$$

Whakaoti mō u

$$u=4$$

$$u=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te u.

$$u\left(6u-24\right)=0$$

Hei kimi otinga whārite, me whakaoti te u=0 me te 6u-24=0.

$$u=0 u=4$$

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.

$$6u^{2}-24u=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, -24 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$u=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 6}$$

Tuhia te pūtakerua o te \left(-24\right)^{2}.

$$u=\frac{-\left(-24\right)±24}{2\times 6}$$

Ko te tauaro o -24 ko 24.

$$u=\frac{24±24}{2\times 6}$$

Whakareatia 2 ki te 6.

$$u=\frac{24±24}{12}$$

Nā, me whakaoti te whārite u=\frac{24±24}{12} ina he tāpiri te ±. Tāpiri 24 ki te 24.

$$u=\frac{48}{12}$$

Whakawehe 48 ki te 12.

$$u=4$$

Nā, me whakaoti te whārite u=\frac{24±24}{12} ina he tango te ±. Tango 24 mai i 24.

$$u=\frac{0}{12}$$

Whakawehe 0 ki te 12.

$$u=0$$

Kua oti te whārite te whakatau.

$$u=4 u=0$$

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.

$$6u^{2}-24u=0$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6u^{2}-24u}{6}=\frac{0}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$u^{2}+\left(-\frac{24}{6}\right)u=\frac{0}{6}$$

Whakawehe -24 ki te 6.

$$u^{2}-4u=\frac{0}{6}$$

Whakawehe 0 ki te 6.

$$u^{2}-4u=0$$

Whakawehea te -4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -2. Nā, tāpiria te pūrua o te -2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$u^{2}-4u+\left(-2\right)^{2}=\left(-2\right)^{2}$$

Pūrua -2.

$$u^{2}-4u+4=4$$

Tauwehea u^{2}-4u+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}.

$$\left(u-2\right)^{2}=4$$

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

$$\sqrt{\left(u-2\right)^{2}}=\sqrt{4}$$

Whakarūnātia.

$$u-2=2 u-2=-2$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$u=4 u=0$$