Whakaoti i te 4x^2-8=0

$$4 x ^ { 2 } - 8 = 0$$

Whakaoti mō x

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

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

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 8 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$4x^{2}=8$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{8}{4}$$

Whakawehea te 8 ki te 4, 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.

$$4x^{2}-8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 0 mō b, me -8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-8\right)}}{2\times 4}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-8\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16\left(-8\right)}}{2\times 4}$$

Whakareatia -16 ki te -8.

$$x=\frac{0±\sqrt{128}}{2\times 4}$$

Tuhia te pūtakerua o te 128.

$$x=\frac{0±8\sqrt{2}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±8\sqrt{2}}{8}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{2}}{8} ina he tāpiri te ±.

$$x=\sqrt{2}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{2}}{8} ina he tango te ±.

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

Kua oti te whārite te whakatau.

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