Whakaoti i te 3x^2-6=0

$$3 { x }^{ 2 } -6=0$$

Whakaoti mō x

$$x=\sqrt{2}\approx 1.414213562$$

$$x=-\sqrt{2}\approx -1.414213562$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 6 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$3x^{2}=6$$

Whakawehea ngā taha e rua ki te 3.

$$x^{2}=\frac{6}{3}$$

Whakawehea te 6 ki te 3, kia riro ko 2.

$$x^{2}=2$$

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

$$x=\sqrt{2} x=-\sqrt{2}$$

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.

$$3x^{2}-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-6\right)}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-6\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\left(-6\right)}}{2\times 3}$$

Whakareatia -12 ki te -6.

$$x=\frac{0±\sqrt{72}}{2\times 3}$$

Tuhia te pūtakerua o te 72.

$$x=\frac{0±6\sqrt{2}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±6\sqrt{2}}{6}$$

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

$$x=\sqrt{2}$$

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

$$x=-\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{2} x=-\sqrt{2}$$