Whakaoti i te 4/x^2=1/9

$$\frac { 4 } { x ^ { 2 } } = \frac { 1 } { 9 }$$

Whakaoti mō x

$$x=6$$

$$x=-6$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 9x^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x^{2},9.

$$9\times 4=x^{2}$$

Whakareatia te 9 ki te 4, ka 36.

$$36=x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}=36$$

Tangohia te 36 mai i ngā taha e rua.

$$x^{2}-36=0$$

Whakaarohia te x^{2}-36. Tuhia anō te x^{2}-36 hei x^{2}-6^{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).

$$\left(x-6\right)\left(x+6\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-6=0 me te x+6=0.

$$x=6 x=-6$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 9x^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x^{2},9.

$$9\times 4=x^{2}$$

Whakareatia te 9 ki te 4, ka 36.

$$36=x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}=36$$

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

$$x=6 x=-6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 9x^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x^{2},9.

$$9\times 4=x^{2}$$

Whakareatia te 9 ki te 4, ka 36.

$$36=x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}=36$$

Tangohia te 36 mai i ngā taha e rua.

$$x^{2}-36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-36\right)}}{2}$$

Whakareatia -4 ki te -36.

$$x=\frac{0±\sqrt{144}}{2}$$

Tuhia te pūtakerua o te 144.

$$x=\frac{0±12}{2}$$

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

$$x=6$$

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

$$x=-6$$

Kua oti te whārite te whakatau.

$$x=6 x=-6$$