Whakaoti i te 12x^2-16=0

$$12 { x }^{ 2 } -16=0$$

Whakaoti mō x

$$x = \frac{2 \sqrt{3}}{3} \approx 1.154700538$$

$$x = -\frac{2 \sqrt{3}}{3} \approx -1.154700538$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 16 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$12x^{2}=16$$

Whakawehea ngā taha e rua ki te 12.

$$x^{2}=\frac{16}{12}$$

Whakahekea te hautanga \frac{16}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}=\frac{4}{3}$$

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

$$x=\frac{2\sqrt{3}}{3} x=-\frac{2\sqrt{3}}{3}$$

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.

$$12x^{2}-16=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 12 mō a, 0 mō b, me -16 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 12\left(-16\right)}}{2\times 12}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 12\left(-16\right)}}{2\times 12}$$

Whakareatia -4 ki te 12.

$$x=\frac{0±\sqrt{-48\left(-16\right)}}{2\times 12}$$

Whakareatia -48 ki te -16.

$$x=\frac{0±\sqrt{768}}{2\times 12}$$

Tuhia te pūtakerua o te 768.

$$x=\frac{0±16\sqrt{3}}{2\times 12}$$

Whakareatia 2 ki te 12.

$$x=\frac{0±16\sqrt{3}}{24}$$

Nā, me whakaoti te whārite x=\frac{0±16\sqrt{3}}{24} ina he tāpiri te ±.

$$x=\frac{2\sqrt{3}}{3}$$

Nā, me whakaoti te whārite x=\frac{0±16\sqrt{3}}{24} ina he tango te ±.

$$x=-\frac{2\sqrt{3}}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{3}}{3} x=-\frac{2\sqrt{3}}{3}$$