Whakaoti i te 1/3x^2-3=0

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

Whakaoti mō x

$$x=3$$

$$x=-3$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Me whakarea ngā taha e rua ki te 3.

$$x^{2}-9=0$$

Whakaarohia te x^{2}-9. Tuhia anō te x^{2}-9 hei x^{2}-3^{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).

$$\left(x-3\right)\left(x+3\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-3=0 me te x+3=0.

$$x=3 x=-3$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 3 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

Me whakarea ngā taha e rua ki te 3, te tau utu o \frac{1}{3}.

$$x^{2}=3\times 3$$

Whakareatia te 3 ki te 3, ka 9.

$$x^{2}=9$$

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

$$x=3 x=-3$$

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.

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

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

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

Pūrua 0.

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

Whakareatia -4 ki te \frac{1}{3}.

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

Whakareatia -\frac{4}{3} ki te -3.

$$x=\frac{0±\sqrt{4}}{2\times \frac{1}{3}}$$

Tuhia te pūtakerua o te 4.

$$x=\frac{0±2}{2\times \frac{1}{3}}$$

Whakareatia 2 ki te \frac{1}{3}.

$$x=\frac{0±2}{\frac{2}{3}}$$

Nā, me whakaoti te whārite x=\frac{0±2}{\frac{2}{3}} ina he tāpiri te ±. Whakawehe 2 ki te \frac{2}{3} mā te whakarea 2 ki te tau huripoki o \frac{2}{3}.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{0±2}{\frac{2}{3}} ina he tango te ±. Whakawehe -2 ki te \frac{2}{3} mā te whakarea -2 ki te tau huripoki o \frac{2}{3}.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=3 x=-3$$