Whakaoti i te (x+x/1)^2=4

$$( x + \frac { x } { 1 } ) ^ { 2 } = 4$$

Whakaoti mō x

$$x=1$$

$$x=-1$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$\left(x+x\right)^{2}=4$$

Pahekotia te x me x, ka 2x.

$$\left(2x\right)^{2}=4$$

Whakarohaina te \left(2x\right)^{2}.

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Tangohia te 4 mai i ngā taha e rua.

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

Whakawehea ngā taha e rua ki te 4.

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

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

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$\left(x+x\right)^{2}=4$$

Pahekotia te x me x, ka 2x.

$$\left(2x\right)^{2}=4$$

Whakarohaina te \left(2x\right)^{2}.

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Whakawehea ngā taha e rua ki te 4.

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

Whakawehea te 4 ki te 4, 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

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$\left(x+x\right)^{2}=4$$

Pahekotia te x me x, ka 2x.

$$\left(2x\right)^{2}=4$$

Whakarohaina te \left(2x\right)^{2}.

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Tangohia te 4 mai i ngā taha e rua.

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

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

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

Pūrua 0.

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

Whakareatia -4 ki te 4.

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

Whakareatia -16 ki te -4.

$$x=\frac{0±\sqrt{64}}{2\times 4}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{0±8}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±8}{8}$$

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

$$x=1$$

Nā, me whakaoti te whārite x=\frac{0±8}{8} ina he tango te ±. Whakawehe -8 ki te 8.

$$x=-1$$

Kua oti te whārite te whakatau.

$$x=1 x=-1$$