Whakaoti i te {l}{x^2=3/2x-1}{=}

$$\left. \begin{array} { l } { x ^ { 2 } = \frac { 3 } { 2 } x - 1 } \\ { = } \end{array} \right.$$

Whakaoti mō x

$$x=\frac{3+\sqrt{7}i}{4}\approx 0.75+0.661437828i$$

$$x=\frac{-\sqrt{7}i+3}{4}\approx 0.75-0.661437828i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te \frac{3}{2}x mai i ngā taha e rua.

$$x^{2}-\frac{3}{2}x=-1$$

Me tāpiri te 1 ki ngā taha e rua.

$$x^{2}-\frac{3}{2}x+1=0$$

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

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

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

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

Tāpiri \frac{9}{4} ki te -4.

$$x=\frac{-\left(-\frac{3}{2}\right)±\sqrt{-\frac{7}{4}}}{2}$$

Tuhia te pūtakerua o te -\frac{7}{4}.

$$x=\frac{-\left(-\frac{3}{2}\right)±\frac{\sqrt{7}i}{2}}{2}$$

Ko te tauaro o -\frac{3}{2} ko \frac{3}{2}.

$$x=\frac{\frac{3}{2}±\frac{\sqrt{7}i}{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{\frac{3}{2}±\frac{\sqrt{7}i}{2}}{2} ina he tāpiri te ±. Tāpiri \frac{3}{2} ki te \frac{i\sqrt{7}}{2}.

$$x=\frac{3+\sqrt{7}i}{2\times 2}$$

Whakawehe \frac{3+i\sqrt{7}}{2} ki te 2.

$$x=\frac{3+\sqrt{7}i}{4}$$

Nā, me whakaoti te whārite x=\frac{\frac{3}{2}±\frac{\sqrt{7}i}{2}}{2} ina he tango te ±. Tango \frac{i\sqrt{7}}{2} mai i \frac{3}{2}.

$$x=\frac{-\sqrt{7}i+3}{2\times 2}$$

Whakawehe \frac{3-i\sqrt{7}}{2} ki te 2.

$$x=\frac{-\sqrt{7}i+3}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{3+\sqrt{7}i}{4} x=\frac{-\sqrt{7}i+3}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te \frac{3}{2}x mai i ngā taha e rua.

$$x^{2}-\frac{3}{2}x=-1$$

Whakawehea te -\frac{3}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{4}. Nā, tāpiria te pūrua o te -\frac{3}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{3}{2}x+\left(-\frac{3}{4}\right)^{2}=-1+\left(-\frac{3}{4}\right)^{2}$$

Pūruatia -\frac{3}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{3}{2}x+\frac{9}{16}=-1+\frac{9}{16}$$

Tāpiri -1 ki te \frac{9}{16}.

$$x^{2}-\frac{3}{2}x+\frac{9}{16}=-\frac{7}{16}$$

Tauwehea x^{2}-\frac{3}{2}x+\frac{9}{16}. 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}.

$$\left(x-\frac{3}{4}\right)^{2}=-\frac{7}{16}$$

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

$$\sqrt{\left(x-\frac{3}{4}\right)^{2}}=\sqrt{-\frac{7}{16}}$$

Whakarūnātia.

$$x-\frac{3}{4}=\frac{\sqrt{7}i}{4} x-\frac{3}{4}=-\frac{\sqrt{7}i}{4}$$

Me tāpiri \frac{3}{4} ki ngā taha e rua o te whārite.

$$x=\frac{3+\sqrt{7}i}{4} x=\frac{-\sqrt{7}i+3}{4}$$