Whakaoti i te 4x^2-2=16

$$4 x ^ { 2 } - 2 = 16$$

Whakaoti mō x

$$x = \frac{3 \sqrt{2}}{2} \approx 2.121320344$$

$$x = -\frac{3 \sqrt{2}}{2} \approx -2.121320344$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 2 ki ngā taha e rua.

$$4x^{2}=16+2$$

Tāpirihia te 16 ki te 2, ka 18.

$$4x^{2}=18$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{18}{4}$$

Whakahekea te hautanga \frac{18}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}=\frac{9}{2}$$

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

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 16 mai i ngā taha e rua.

$$4x^{2}-2-16=0$$

Tangohia te 16 i te -2, ka -18.

$$4x^{2}-18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 0 mō b, me -18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-18\right)}}{2\times 4}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-18\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16\left(-18\right)}}{2\times 4}$$

Whakareatia -16 ki te -18.

$$x=\frac{0±\sqrt{288}}{2\times 4}$$

Tuhia te pūtakerua o te 288.

$$x=\frac{0±12\sqrt{2}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±12\sqrt{2}}{8}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{2}}{8} ina he tāpiri te ±.

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

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{2}}{8} ina he tango te ±.

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

Kua oti te whārite te whakatau.

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