Whakaoti i te 2(1-3x^2)=0

$$2(1-3 { x }^{ 2 } )=0$$

Whakaoti mō x

$$x=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Ngā Upane mā te Kimi Pūtakerua

Whakawehea ngā taha e rua ki te 2. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$1-3x^{2}=0$$

Tangohia te 1 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Whakawehea ngā taha e rua ki te -3.

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

Ka taea te hautanga \frac{-1}{-3} te whakamāmā ki te \frac{1}{3} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

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

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

$$x=\frac{\sqrt{3}}{3} x=-\frac{\sqrt{3}}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ngā taha e rua ki te 2. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$1-3x^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

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

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)}}{2\left(-3\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{0±\sqrt{12}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 12.

$$x=\frac{0±2\sqrt{3}}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{0±2\sqrt{3}}{-6}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{3}}{-6} ina he tāpiri te ±.

$$x=-\frac{\sqrt{3}}{3}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{3}}{-6} ina he tango te ±.

$$x=\frac{\sqrt{3}}{3}$$

Kua oti te whārite te whakatau.

$$x=-\frac{\sqrt{3}}{3} x=\frac{\sqrt{3}}{3}$$