Whakaoti i te 3-4x^2=5-6x^2

$$3 - 4 x ^ { 2 } = 5 - 6 x ^ { 2 }$$

Whakaoti mō x

$$x=1$$

$$x=-1$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tangohia te 5 mai i ngā taha e rua.

$$3-4x^{2}-5=-6x^{2}$$

Tangohia te 5 i te 3, ka -2.

$$-2-4x^{2}=-6x^{2}$$

Me tāpiri te 6x^{2} ki ngā taha e rua.

$$-2-4x^{2}+6x^{2}=0$$

Pahekotia te -4x^{2} me 6x^{2}, ka 2x^{2}.

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

Whakawehea ngā taha e rua ki te 2.

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

Whakaarohia te -1+x^{2}. Tuhia anō te -1+x^{2} hei x^{2}-1^{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).

$$\left(x-1\right)\left(x+1\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-1=0 me te x+1=0.

$$x=1 x=-1$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 6x^{2} ki ngā taha e rua.

$$3-4x^{2}+6x^{2}=5$$

Pahekotia te -4x^{2} me 6x^{2}, ka 2x^{2}.

$$3+2x^{2}=5$$

Tangohia te 3 mai i ngā taha e rua.

$$2x^{2}=5-3$$

Tangohia te 3 i te 5, ka 2.

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

Whakawehea ngā taha e rua ki te 2.

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

Whakawehea te 2 ki te 2, kia riro ko 1.

$$x^{2}=1$$

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

$$x=1 x=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 5 mai i ngā taha e rua.

$$3-4x^{2}-5=-6x^{2}$$

Tangohia te 5 i te 3, ka -2.

$$-2-4x^{2}=-6x^{2}$$

Me tāpiri te 6x^{2} ki ngā taha e rua.

$$-2-4x^{2}+6x^{2}=0$$

Pahekotia te -4x^{2} me 6x^{2}, ka 2x^{2}.

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

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.

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

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

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

Pūrua 0.

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

Whakareatia -4 ki te 2.

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

Whakareatia -8 ki te -2.

$$x=\frac{0±\sqrt{16}}{2\times 2}$$

Tuhia te pūtakerua o te 16.

$$x=\frac{0±4}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±4}{4}$$

Nā, me whakaoti te whārite x=\frac{0±4}{4} ina he tāpiri te ±. Whakawehe 4 ki te 4.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{0±4}{4} ina he tango te ±. Whakawehe -4 ki te 4.

$$x=-1$$

Kua oti te whārite te whakatau.

$$x=1 x=-1$$