Whakaoti i te 3x^2+4x^2=7

$$3 x ^ { 2 } + 4 x ^ { 2 } = 7$$

Whakaoti mō x

$$x=1$$

$$x=-1$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Pahekotia te 3x^{2} me 4x^{2}, ka 7x^{2}.

$$7x^{2}=7$$

Tangohia te 7 mai i ngā taha e rua.

$$7x^{2}-7=0$$

Whakawehea ngā taha e rua ki te 7.

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

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

Pahekotia te 3x^{2} me 4x^{2}, ka 7x^{2}.

$$7x^{2}=7$$

Whakawehea ngā taha e rua ki te 7.

$$x^{2}=\frac{7}{7}$$

Whakawehea te 7 ki te 7, 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

Pahekotia te 3x^{2} me 4x^{2}, ka 7x^{2}.

$$7x^{2}=7$$

Tangohia te 7 mai i ngā taha e rua.

$$7x^{2}-7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 7 mō a, 0 mō b, me -7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-7\right)}}{2\times 7}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 7\left(-7\right)}}{2\times 7}$$

Whakareatia -4 ki te 7.

$$x=\frac{0±\sqrt{-28\left(-7\right)}}{2\times 7}$$

Whakareatia -28 ki te -7.

$$x=\frac{0±\sqrt{196}}{2\times 7}$$

Tuhia te pūtakerua o te 196.

$$x=\frac{0±14}{2\times 7}$$

Whakareatia 2 ki te 7.

$$x=\frac{0±14}{14}$$

Nā, me whakaoti te whārite x=\frac{0±14}{14} ina he tāpiri te ±. Whakawehe 14 ki te 14.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{0±14}{14} ina he tango te ±. Whakawehe -14 ki te 14.

$$x=-1$$

Kua oti te whārite te whakatau.

$$x=1 x=-1$$