Whakaoti i te 1/100=1/t+480+1/t

$$\frac{ 1 }{ 100 } = \frac{ 1 }{ t+480 } + \frac{ 1 }{ t }$$

Whakaoti mō t

$$t=-400$$

$$t=120$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe t ki tētahi o ngā uara -480,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 100t\left(t+480\right), arā, te tauraro pātahi he tino iti rawa te kitea o 100,t+480,t.

$$t\left(t+480\right)=100t+100t+48000$$

Whakamahia te āhuatanga tohatoha hei whakarea te t ki te t+480.

$$t^{2}+480t=100t+100t+48000$$

Pahekotia te 100t me 100t, ka 200t.

$$t^{2}+480t=200t+48000$$

Tangohia te 200t mai i ngā taha e rua.

$$t^{2}+480t-200t=48000$$

Pahekotia te 480t me -200t, ka 280t.

$$t^{2}+280t=48000$$

Tangohia te 48000 mai i ngā taha e rua.

$$t^{2}+280t-48000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 280 mō b, me -48000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-280±\sqrt{280^{2}-4\left(-48000\right)}}{2}$$

Pūrua 280.

$$t=\frac{-280±\sqrt{78400-4\left(-48000\right)}}{2}$$

Whakareatia -4 ki te -48000.

$$t=\frac{-280±\sqrt{78400+192000}}{2}$$

Tāpiri 78400 ki te 192000.

$$t=\frac{-280±\sqrt{270400}}{2}$$

Tuhia te pūtakerua o te 270400.

$$t=\frac{-280±520}{2}$$

Nā, me whakaoti te whārite t=\frac{-280±520}{2} ina he tāpiri te ±. Tāpiri -280 ki te 520.

$$t=\frac{240}{2}$$

Whakawehe 240 ki te 2.

$$t=120$$

Nā, me whakaoti te whārite t=\frac{-280±520}{2} ina he tango te ±. Tango 520 mai i -280.

$$t=-\frac{800}{2}$$

Whakawehe -800 ki te 2.

$$t=-400$$

Kua oti te whārite te whakatau.

$$t=120 t=-400$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe t ki tētahi o ngā uara -480,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 100t\left(t+480\right), arā, te tauraro pātahi he tino iti rawa te kitea o 100,t+480,t.

$$t\left(t+480\right)=100t+100t+48000$$

Whakamahia te āhuatanga tohatoha hei whakarea te t ki te t+480.

$$t^{2}+480t=100t+100t+48000$$

Pahekotia te 100t me 100t, ka 200t.

$$t^{2}+480t=200t+48000$$

Tangohia te 200t mai i ngā taha e rua.

$$t^{2}+480t-200t=48000$$

Pahekotia te 480t me -200t, ka 280t.

$$t^{2}+280t=48000$$

Whakawehea te 280, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 140. Nā, tāpiria te pūrua o te 140 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}+280t+140^{2}=48000+140^{2}$$

Pūrua 140.

$$t^{2}+280t+19600=48000+19600$$

Tāpiri 48000 ki te 19600.

$$t^{2}+280t+19600=67600$$

Tauwehea te t^{2}+280t+19600. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(t+140\right)^{2}=67600$$

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

$$\sqrt{\left(t+140\right)^{2}}=\sqrt{67600}$$

Whakarūnātia.

$$t+140=260 t+140=-260$$

Me tango 140 mai i ngā taha e rua o te whārite.

$$t=120 t=-400$$