Whakaoti i te 1/2x^2=x

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

Whakaoti mō x

$$x=2$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te x mai i ngā taha e rua.

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

Tauwehea te x.

$$x\left(\frac{1}{2}x-1\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te \frac{x}{2}-1=0.

$$x=0 x=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te x mai i ngā taha e rua.

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

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

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

Tuhia te pūtakerua o te 1.

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

Ko te tauaro o -1 ko 1.

$$x=\frac{1±1}{2\times \frac{1}{2}}$$

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

$$x=\frac{1±1}{1}$$

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

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

Whakawehe 2 ki te 1.

$$x=2$$

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

$$x=\frac{0}{1}$$

Whakawehe 0 ki te 1.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=2 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te x mai i ngā taha e rua.

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

Me whakarea ngā taha e rua ki te 2.

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

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

$$x^{2}+\left(-\frac{1}{\frac{1}{2}}\right)x=\frac{0}{\frac{1}{2}}$$

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

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

Whakawehe 0 ki te \frac{1}{2} mā te whakarea 0 ki te tau huripoki o \frac{1}{2}.

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

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.

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

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}.

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

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

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

Whakarūnātia.

$$x-1=1 x-1=-1$$

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

$$x=2 x=0$$