Whakaoti i te 3x^2-48=0

$$3 x ^ { 2 } - 48 = 0$$

Whakaoti mō x

$$x=4$$

$$x=-4$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te 3.

$$x^{2}-16=0$$

Whakaarohia te x^{2}-16. Tuhia anō te x^{2}-16 hei x^{2}-4^{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).

$$\left(x-4\right)\left(x+4\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-4=0 me te x+4=0.

$$x=4 x=-4$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 48 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$3x^{2}=48$$

Whakawehea ngā taha e rua ki te 3.

$$x^{2}=\frac{48}{3}$$

Whakawehea te 48 ki te 3, kia riro ko 16.

$$x^{2}=16$$

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

$$x=4 x=-4$$

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.

$$3x^{2}-48=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me -48 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-48\right)}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-48\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\left(-48\right)}}{2\times 3}$$

Whakareatia -12 ki te -48.

$$x=\frac{0±\sqrt{576}}{2\times 3}$$

Tuhia te pūtakerua o te 576.

$$x=\frac{0±24}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±24}{6}$$

Nā, me whakaoti te whārite x=\frac{0±24}{6} ina he tāpiri te ±. Whakawehe 24 ki te 6.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{0±24}{6} ina he tango te ±. Whakawehe -24 ki te 6.

$$x=-4$$

Kua oti te whārite te whakatau.

$$x=4 x=-4$$