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

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

Whakaoti mō t

$$t=80$$

$$t=600$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe t ki tētahi o ngā uara 0,480 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 -680t.

$$t^{2}-680t=-48000$$

Me tāpiri te 48000 ki ngā taha e rua.

$$t^{2}-680t+48000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -680 mō b, me 48000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-680\right)±\sqrt{\left(-680\right)^{2}-4\times 48000}}{2}$$

Pūrua -680.

$$t=\frac{-\left(-680\right)±\sqrt{462400-4\times 48000}}{2}$$

Whakareatia -4 ki te 48000.

$$t=\frac{-\left(-680\right)±\sqrt{462400-192000}}{2}$$

Tāpiri 462400 ki te -192000.

$$t=\frac{-\left(-680\right)±\sqrt{270400}}{2}$$

Tuhia te pūtakerua o te 270400.

$$t=\frac{-\left(-680\right)±520}{2}$$

Ko te tauaro o -680 ko 680.

$$t=\frac{680±520}{2}$$

Nā, me whakaoti te whārite t=\frac{680±520}{2} ina he tāpiri te ±. Tāpiri 680 ki te 520.

$$t=\frac{1200}{2}$$

Whakawehe 1200 ki te 2.

$$t=600$$

Nā, me whakaoti te whārite t=\frac{680±520}{2} ina he tango te ±. Tango 520 mai i 680.

$$t=\frac{160}{2}$$

Whakawehe 160 ki te 2.

$$t=80$$

Kua oti te whārite te whakatau.

$$t=600 t=80$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe t ki tētahi o ngā uara 0,480 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 -680t.

$$t^{2}-680t=-48000$$

Whakawehea te -680, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -340. Nā, tāpiria te pūrua o te -340 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-680t+\left(-340\right)^{2}=-48000+\left(-340\right)^{2}$$

Pūrua -340.

$$t^{2}-680t+115600=-48000+115600$$

Tāpiri -48000 ki te 115600.

$$t^{2}-680t+115600=67600$$

Tauwehea te t^{2}-680t+115600. 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}.

$$\left(t-340\right)^{2}=67600$$

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

$$\sqrt{\left(t-340\right)^{2}}=\sqrt{67600}$$

Whakarūnātia.

$$t-340=260 t-340=-260$$

Me tāpiri 340 ki ngā taha e rua o te whārite.

$$t=600 t=80$$