Whakaoti i te 3x^2-1=0

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

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

Me tāpiri te 1 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

Whakawehea ngā taha e rua ki te 3.

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

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

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}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-1\right)}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-1\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\left(-1\right)}}{2\times 3}$$

Whakareatia -12 ki te -1.

$$x=\frac{0±\sqrt{12}}{2\times 3}$$

Tuhia te pūtakerua o te 12.

$$x=\frac{0±2\sqrt{3}}{2\times 3}$$

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.

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