Whakaoti i te 0=1/2x^2-x-2

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

Whakaoti mō x

$$x=\sqrt{5}+1\approx 3.236067977$$

$$x=1-\sqrt{5}\approx -1.236067977$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

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

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

Whakareatia -4 ki te \frac{1}{2}.

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

Whakareatia -2 ki te -2.

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

Tāpiri 1 ki te 4.

$$x=\frac{-\left(-1\right)±\sqrt{5}}{2\times \frac{1}{2}}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±\sqrt{5}}{2\times \frac{1}{2}}$$

Whakareatia 2 ki te \frac{1}{2}.

$$x=\frac{1±\sqrt{5}}{1}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{5}}{1} ina he tāpiri te ±. Tāpiri 1 ki te \sqrt{5}.

$$x=\frac{\sqrt{5}+1}{1}$$

Whakawehe 1+\sqrt{5} ki te 1.

$$x=\sqrt{5}+1$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{5}}{1} ina he tango te ±. Tango \sqrt{5} mai i 1.

$$x=\frac{1-\sqrt{5}}{1}$$

Whakawehe 1-\sqrt{5} ki te 1.

$$x=1-\sqrt{5}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{5}+1 x=1-\sqrt{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Me tāpiri te 2 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

Me whakarea ngā taha e rua ki te 2.

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

Mā te whakawehe ki te \frac{1}{2} ka wetekia te whakareanga ki te \frac{1}{2}.

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

Whakawehe -1 ki te \frac{1}{2} mā te whakarea -1 ki te tau huripoki o \frac{1}{2}.

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

Whakawehe 2 ki te \frac{1}{2} mā te whakarea 2 ki te tau huripoki o \frac{1}{2}.

$$x^{2}-2x=4$$

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

$$x^{2}-2x+1=4+1$$

Tāpiri 4 ki te 1.

$$x^{2}-2x+1=5$$

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

$$\left(x-1\right)^{2}=5$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{5}$$

Whakarūnātia.

$$x-1=\sqrt{5} x-1=-\sqrt{5}$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=\sqrt{5}+1 x=1-\sqrt{5}$$