Whakaoti i te z*5z=5

$$z \times 5z=5$$

Whakaoti mō z

$$z=1$$

$$z=-1$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te z ki te z, ka z^{2}.

$$z^{2}\times 5=5$$

Whakawehea ngā taha e rua ki te 5.

$$z^{2}=\frac{5}{5}$$

Whakawehea te 5 ki te 5, kia riro ko 1.

$$z^{2}=1$$

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

$$z=1 z=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te z ki te z, ka z^{2}.

$$z^{2}\times 5=5$$

Tangohia te 5 mai i ngā taha e rua.

$$z^{2}\times 5-5=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$5z^{2}-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 0 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\times 5\left(-5\right)}}{2\times 5}$$

Pūrua 0.

$$z=\frac{0±\sqrt{-4\times 5\left(-5\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$z=\frac{0±\sqrt{-20\left(-5\right)}}{2\times 5}$$

Whakareatia -20 ki te -5.

$$z=\frac{0±\sqrt{100}}{2\times 5}$$

Tuhia te pūtakerua o te 100.

$$z=\frac{0±10}{2\times 5}$$

Whakareatia 2 ki te 5.

$$z=\frac{0±10}{10}$$

Nā, me whakaoti te whārite z=\frac{0±10}{10} ina he tāpiri te ±. Whakawehe 10 ki te 10.

$$z=1$$

Nā, me whakaoti te whārite z=\frac{0±10}{10} ina he tango te ±. Whakawehe -10 ki te 10.

$$z=-1$$

Kua oti te whārite te whakatau.

$$z=1 z=-1$$