Whakaoti i te z^2-3z+9/4=0

$$z ^ { 2 } - 3 z + \frac { 9 } { 4 } = 0$$

Whakaoti mō z

$$z = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

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.

$$z^{2}-3z+\frac{9}{4}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -3 mō b, me \frac{9}{4} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times \frac{9}{4}}}{2}$$

Pūrua -3.

$$z=\frac{-\left(-3\right)±\sqrt{9-4\times \frac{9}{4}}}{2}$$

Whakareatia -4 ki te \frac{9}{4}.

$$z=\frac{-\left(-3\right)±\sqrt{9-9}}{2}$$

Tāpiri 9 ki te -9.

$$z=\frac{-\left(-3\right)±\sqrt{0}}{2}$$

Tuhia te pūtakerua o te 0.

$$z=-\frac{-3}{2}$$

Ko te tauaro o -3 ko 3.

$$z=\frac{3}{2}$$

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.

$$z^{2}-3z+\frac{9}{4}=0$$

Tauwehea z^{2}-3z+\frac{9}{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}.

$$\left(z-\frac{3}{2}\right)^{2}=0$$

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

$$\sqrt{\left(z-\frac{3}{2}\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$z-\frac{3}{2}=0 z-\frac{3}{2}=0$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$z=\frac{3}{2} z=\frac{3}{2}$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$z=\frac{3}{2}$$