Whakaoti i te -t^2+4t-280/t^2-4t=0

$$\frac{ - { t }^{ 2 } +4t-280 }{ { t }^{ 2 } -4t } = 0$$

Whakaoti mō t

$$t=-2\sqrt{69}i+2\approx 2-16.613247726i$$

$$t=2+2\sqrt{69}i\approx 2+16.613247726i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe t ki tētahi o ngā uara 0,4 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te t\left(t-4\right).

$$-t^{2}+4t-280=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 4 mō b, me -280 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-4±\sqrt{4^{2}-4\left(-1\right)\left(-280\right)}}{2\left(-1\right)}$$

Pūrua 4.

$$t=\frac{-4±\sqrt{16-4\left(-1\right)\left(-280\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$t=\frac{-4±\sqrt{16+4\left(-280\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -280.

$$t=\frac{-4±\sqrt{16-1120}}{2\left(-1\right)}$$

Tāpiri 16 ki te -1120.

$$t=\frac{-4±\sqrt{-1104}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te -1104.

$$t=\frac{-4±4\sqrt{69}i}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$t=\frac{-4±4\sqrt{69}i}{-2}$$

Nā, me whakaoti te whārite t=\frac{-4±4\sqrt{69}i}{-2} ina he tāpiri te ±. Tāpiri -4 ki te 4i\sqrt{69}.

$$t=\frac{-4+4\sqrt{69}i}{-2}$$

Whakawehe -4+4i\sqrt{69} ki te -2.

$$t=-2\sqrt{69}i+2$$

Nā, me whakaoti te whārite t=\frac{-4±4\sqrt{69}i}{-2} ina he tango te ±. Tango 4i\sqrt{69} mai i -4.

$$t=\frac{-4\sqrt{69}i-4}{-2}$$

Whakawehe -4-4i\sqrt{69} ki te -2.

$$t=2+2\sqrt{69}i$$

Kua oti te whārite te whakatau.

$$t=-2\sqrt{69}i+2 t=2+2\sqrt{69}i$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe t ki tētahi o ngā uara 0,4 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te t\left(t-4\right).

$$-t^{2}+4t-280=0$$

Me tāpiri te 280 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$-t^{2}+4t=280$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-t^{2}+4t}{-1}=\frac{280}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$t^{2}+\frac{4}{-1}t=\frac{280}{-1}$$

Whakawehe 4 ki te -1.

$$t^{2}-4t=\frac{280}{-1}$$

Whakawehe 280 ki te -1.

$$t^{2}-4t=-280$$

Whakawehea te -4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -2. Nā, tāpiria te pūrua o te -2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-4t+\left(-2\right)^{2}=-280+\left(-2\right)^{2}$$

Pūrua -2.

$$t^{2}-4t+4=-280+4$$

Tāpiri -280 ki te 4.

$$t^{2}-4t+4=-276$$

Tauwehea t^{2}-4t+4. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(t-2\right)^{2}=-276$$

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

$$\sqrt{\left(t-2\right)^{2}}=\sqrt{-276}$$

Whakarūnātia.

$$t-2=2\sqrt{69}i t-2=-2\sqrt{69}i$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$t=2+2\sqrt{69}i t=-2\sqrt{69}i+2$$