Whakaoti i te 2x^2-1=4

$$2 x ^ { 2 } - 1 = 4$$

Whakaoti mō x

$$x = \frac{\sqrt{10}}{2} \approx 1.58113883$$

$$x = -\frac{\sqrt{10}}{2} \approx -1.58113883$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 1 ki ngā taha e rua.

$$2x^{2}=4+1$$

Tāpirihia te 4 ki te 1, ka 5.

$$2x^{2}=5$$

Whakawehea ngā taha e rua ki te 2.

$$x^{2}=\frac{5}{2}$$

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

$$x=\frac{\sqrt{10}}{2} x=-\frac{\sqrt{10}}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 4 mai i ngā taha e rua.

$$2x^{2}-1-4=0$$

Tangohia te 4 i te -1, ka -5.

$$2x^{2}-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-5\right)}}{2\times 2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-5\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\left(-5\right)}}{2\times 2}$$

Whakareatia -8 ki te -5.

$$x=\frac{0±\sqrt{40}}{2\times 2}$$

Tuhia te pūtakerua o te 40.

$$x=\frac{0±2\sqrt{10}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±2\sqrt{10}}{4}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{10}}{4} ina he tāpiri te ±.

$$x=\frac{\sqrt{10}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{10}}{4} ina he tango te ±.

$$x=-\frac{\sqrt{10}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{10}}{2} x=-\frac{\sqrt{10}}{2}$$