Whakaoti i te (x+3)(x-3)=5

$$( x + 3 ) ( x - 3 ) = 5$$

Whakaoti mō x

$$x=\sqrt{14}\approx 3.741657387$$

$$x=-\sqrt{14}\approx -3.741657387$$

Ngā Upane mā te Kimi Pūtakerua

Whakaarohia te \left(x+3\right)\left(x-3\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 3.

$$x^{2}-9=5$$

Me tāpiri te 9 ki ngā taha e rua.

$$x^{2}=5+9$$

Tāpirihia te 5 ki te 9, ka 14.

$$x^{2}=14$$

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

$$x=\sqrt{14} x=-\sqrt{14}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakaarohia te \left(x+3\right)\left(x-3\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 3.

$$x^{2}-9=5$$

Tangohia te 5 mai i ngā taha e rua.

$$x^{2}-9-5=0$$

Tangohia te 5 i te -9, ka -14.

$$x^{2}-14=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -14 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-14\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-14\right)}}{2}$$

Whakareatia -4 ki te -14.

$$x=\frac{0±\sqrt{56}}{2}$$

Tuhia te pūtakerua o te 56.

$$x=\frac{0±2\sqrt{14}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{14}}{2} ina he tāpiri te ±.

$$x=\sqrt{14}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{14}}{2} ina he tango te ±.

$$x=-\sqrt{14}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{14} x=-\sqrt{14}$$