Whakaoti i te x^2=x+3

$$x ^ { 2 } = x + 3$$

Whakaoti mō x

$$x = \frac{\sqrt{13} + 1}{2} \approx 2.302775638$$

$$x=\frac{1-\sqrt{13}}{2}\approx -1.302775638$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te x mai i ngā taha e rua.

$$x^{2}-x=3$$

Tangohia te 3 mai i ngā taha e rua.

$$x^{2}-x-3=0$$

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

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

Whakareatia -4 ki te -3.

$$x=\frac{-\left(-1\right)±\sqrt{1+12}}{2}$$

Tāpiri 1 ki te 12.

$$x=\frac{-\left(-1\right)±\sqrt{13}}{2}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±\sqrt{13}}{2}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{13}}{2} ina he tāpiri te ±. Tāpiri 1 ki te \sqrt{13}.

$$x=\frac{\sqrt{13}+1}{2}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{13}}{2} ina he tango te ±. Tango \sqrt{13} mai i 1.

$$x=\frac{1-\sqrt{13}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{13}+1}{2} x=\frac{1-\sqrt{13}}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te x mai i ngā taha e rua.

$$x^{2}-x=3$$

Whakawehea te -1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{2}. Nā, tāpiria te pūrua o te -\frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-x+\frac{1}{4}=3+\frac{1}{4}$$

Tāpiri 3 ki te \frac{1}{4}.

$$x^{2}-x+\frac{1}{4}=\frac{13}{4}$$

Tauwehea x^{2}-x+\frac{1}{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}.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{13}{4}$$

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

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{13}{4}}$$

Whakarūnātia.

$$x-\frac{1}{2}=\frac{\sqrt{13}}{2} x-\frac{1}{2}=-\frac{\sqrt{13}}{2}$$

Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{13}+1}{2} x=\frac{1-\sqrt{13}}{2}$$