Whakaoti i te 4x^2=1

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

Whakaoti mō x

$$x=\frac{1}{2}=0.5$$

$$x=-\frac{1}{2}=-0.5$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{1}{4}$$

Tangohia te \frac{1}{4} mai i ngā taha e rua.

$$x^{2}-\frac{1}{4}=0$$

Me whakarea ngā taha e rua ki te 4.

$$4x^{2}-1=0$$

Whakaarohia te 4x^{2}-1. Tuhia anō te 4x^{2}-1 hei \left(2x\right)^{2}-1^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-1\right)\left(2x+1\right)=0$$

Hei kimi otinga whārite, me whakaoti te 2x-1=0 me te 2x+1=0.

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

Ngā Upane mā te Kimi Pūtakerua

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{1}{4}$$

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

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{1}{4}$$

Tangohia te \frac{1}{4} mai i ngā taha e rua.

$$x^{2}-\frac{1}{4}=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{4}\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{4}\right)}}{2}$$

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

$$x=\frac{0±\sqrt{1}}{2}$$

Tuhia te pūtakerua o te 1.

$$x=\frac{0±1}{2}$$

Nā, me whakaoti te whārite x=\frac{0±1}{2} ina he tāpiri te ±. Whakawehe 1 ki te 2.

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

Nā, me whakaoti te whārite x=\frac{0±1}{2} ina he tango te ±. Whakawehe -1 ki te 2.

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

Kua oti te whārite te whakatau.

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