Whakaoti i te (x-1)(x+1)=15

$$(x-1)(x+1)=15$$

Whakaoti mō x

$$x=-4$$

$$x=4$$

Ngā Upane mā te Kimi Pūtakerua

Whakaarohia te \left(x-1\right)\left(x+1\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 1.

$$x^{2}-1=15$$

Me tāpiri te 1 ki ngā taha e rua.

$$x^{2}=15+1$$

Tāpirihia te 15 ki te 1, ka 16.

$$x^{2}=16$$

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

$$x=4 x=-4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakaarohia te \left(x-1\right)\left(x+1\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 1.

$$x^{2}-1=15$$

Tangohia te 15 mai i ngā taha e rua.

$$x^{2}-1-15=0$$

Tangohia te 15 i te -1, ka -16.

$$x^{2}-16=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -16 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua 0.

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

Whakareatia -4 ki te -16.

$$x=\frac{0±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{0±8}{2}$$

Nā, me whakaoti te whārite x=\frac{0±8}{2} ina he tāpiri te ±. Whakawehe 8 ki te 2.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{0±8}{2} ina he tango te ±. Whakawehe -8 ki te 2.

$$x=-4$$

Kua oti te whārite te whakatau.

$$x=4 x=-4$$