Whakaoti i te (4+x)*(4-x)=33

$$(4+x) \times (4-x)=33$$

Whakaoti mō x (complex solution)

$$x=-\sqrt{17}i\approx -0-4.123105626i$$

$$x=\sqrt{17}i\approx 4.123105626i$$

Ngā Upane mā te Kimi Pūtakerua

Whakaarohia te \left(4+x\right)\left(4-x\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 4.

$$16-x^{2}=33$$

Tangohia te 16 mai i ngā taha e rua.

$$-x^{2}=33-16$$

Tangohia te 16 i te 33, ka 17.

$$-x^{2}=17$$

Whakawehea ngā taha e rua ki te -1.

$$x^{2}=-17$$

Kua oti te whārite te whakatau.

$$x=\sqrt{17}i x=-\sqrt{17}i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakaarohia te \left(4+x\right)\left(4-x\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 4.

$$16-x^{2}=33$$

Tangohia te 33 mai i ngā taha e rua.

$$16-x^{2}-33=0$$

Tangohia te 33 i te 16, ka -17.

$$-17-x^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$-x^{2}-17=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 0 mō b, me -17 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-17\right)}}{2\left(-1\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-17\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{0±\sqrt{4\left(-17\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -17.

$$x=\frac{0±\sqrt{-68}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te -68.

$$x=\frac{0±2\sqrt{17}i}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{0±2\sqrt{17}i}{-2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{17}i}{-2} ina he tāpiri te ±.

$$x=-\sqrt{17}i$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{17}i}{-2} ina he tango te ±.

$$x=\sqrt{17}i$$

Kua oti te whārite te whakatau.

$$x=-\sqrt{17}i x=\sqrt{17}i$$