Whakaoti i te z^2-1/4=0

$$z ^ { 2 } - \frac { 1 } { 4 } = 0$$

Whakaoti mō z

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

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

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Me whakarea ngā taha e rua ki te 4.

$$4z^{2}-1=0$$

Whakaarohia te 4z^{2}-1. Tuhia anō te 4z^{2}-1 hei \left(2z\right)^{2}-1^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2z-1\right)\left(2z+1\right)=0$$

Hei kimi otinga whārite, me whakaoti te 2z-1=0 me te 2z+1=0.

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

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te \frac{1}{4} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$z^{2}=\frac{1}{4}$$

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

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$z^{2}-\frac{1}{4}=0$$

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

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

Pūrua 0.

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

Whakareatia -4 ki te -\frac{1}{4}.

$$z=\frac{0±\sqrt{1}}{2}$$

Tuhia te pūtakerua o te 1.

$$z=\frac{0±1}{2}$$

Nā, me whakaoti te whārite z=\frac{0±1}{2} ina he tāpiri te ±. Whakawehe 1 ki te 2.

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

Nā, me whakaoti te whārite z=\frac{0±1}{2} ina he tango te ±. Whakawehe -1 ki te 2.

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

Kua oti te whārite te whakatau.

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