Whakaoti i te 1200/a=1200/(a-20)+5

$$\frac { 1200 } { a } = \frac { 1200 } { ( a - 20 ) } + 5$$

Whakaoti mō a

$$a=-10\sqrt{47}i+10\approx 10-68.556546004i$$

$$a=10+10\sqrt{47}i\approx 10+68.556546004i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe a ki tētahi o ngā uara 0,20 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te a\left(a-20\right), arā, te tauraro pātahi he tino iti rawa te kitea o a,a-20.

$$\left(a-20\right)\times 1200=a\times 1200+a\left(a-20\right)\times 5$$

Whakamahia te āhuatanga tohatoha hei whakarea te a-20 ki te 1200.

$$1200a-24000=a\times 1200+a\left(a-20\right)\times 5$$

Whakamahia te āhuatanga tohatoha hei whakarea te a ki te a-20.

$$1200a-24000=a\times 1200+\left(a^{2}-20a\right)\times 5$$

Whakamahia te āhuatanga tohatoha hei whakarea te a^{2}-20a ki te 5.

$$1200a-24000=a\times 1200+5a^{2}-100a$$

Pahekotia te a\times 1200 me -100a, ka 1100a.

$$1200a-24000=1100a+5a^{2}$$

Tangohia te 1100a mai i ngā taha e rua.

$$1200a-24000-1100a=5a^{2}$$

Pahekotia te 1200a me -1100a, ka 100a.

$$100a-24000=5a^{2}$$

Tangohia te 5a^{2} mai i ngā taha e rua.

$$100a-24000-5a^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-5a^{2}+100a-24000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -5 mō a, 100 mō b, me -24000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-100±\sqrt{100^{2}-4\left(-5\right)\left(-24000\right)}}{2\left(-5\right)}$$

Pūrua 100.

$$a=\frac{-100±\sqrt{10000-4\left(-5\right)\left(-24000\right)}}{2\left(-5\right)}$$

Whakareatia -4 ki te -5.

$$a=\frac{-100±\sqrt{10000+20\left(-24000\right)}}{2\left(-5\right)}$$

Whakareatia 20 ki te -24000.

$$a=\frac{-100±\sqrt{10000-480000}}{2\left(-5\right)}$$

Tāpiri 10000 ki te -480000.

$$a=\frac{-100±\sqrt{-470000}}{2\left(-5\right)}$$

Tuhia te pūtakerua o te -470000.

$$a=\frac{-100±100\sqrt{47}i}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$a=\frac{-100±100\sqrt{47}i}{-10}$$

Nā, me whakaoti te whārite a=\frac{-100±100\sqrt{47}i}{-10} ina he tāpiri te ±. Tāpiri -100 ki te 100i\sqrt{47}.

$$a=\frac{-100+100\sqrt{47}i}{-10}$$

Whakawehe -100+100i\sqrt{47} ki te -10.

$$a=-10\sqrt{47}i+10$$

Nā, me whakaoti te whārite a=\frac{-100±100\sqrt{47}i}{-10} ina he tango te ±. Tango 100i\sqrt{47} mai i -100.

$$a=\frac{-100\sqrt{47}i-100}{-10}$$

Whakawehe -100-100i\sqrt{47} ki te -10.

$$a=10+10\sqrt{47}i$$

Kua oti te whārite te whakatau.

$$a=-10\sqrt{47}i+10 a=10+10\sqrt{47}i$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe a ki tētahi o ngā uara 0,20 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te a\left(a-20\right), arā, te tauraro pātahi he tino iti rawa te kitea o a,a-20.

$$\left(a-20\right)\times 1200=a\times 1200+a\left(a-20\right)\times 5$$

Whakamahia te āhuatanga tohatoha hei whakarea te a-20 ki te 1200.

$$1200a-24000=a\times 1200+a\left(a-20\right)\times 5$$

Whakamahia te āhuatanga tohatoha hei whakarea te a ki te a-20.

$$1200a-24000=a\times 1200+\left(a^{2}-20a\right)\times 5$$

Whakamahia te āhuatanga tohatoha hei whakarea te a^{2}-20a ki te 5.

$$1200a-24000=a\times 1200+5a^{2}-100a$$

Pahekotia te a\times 1200 me -100a, ka 1100a.

$$1200a-24000=1100a+5a^{2}$$

Tangohia te 1100a mai i ngā taha e rua.

$$1200a-24000-1100a=5a^{2}$$

Pahekotia te 1200a me -1100a, ka 100a.

$$100a-24000=5a^{2}$$

Tangohia te 5a^{2} mai i ngā taha e rua.

$$100a-24000-5a^{2}=0$$

Me tāpiri te 24000 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$100a-5a^{2}=24000$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-5a^{2}+100a=24000$$

Whakawehea ngā taha e rua ki te -5.

$$\frac{-5a^{2}+100a}{-5}=\frac{24000}{-5}$$

Mā te whakawehe ki te -5 ka wetekia te whakareanga ki te -5.

$$a^{2}+\frac{100}{-5}a=\frac{24000}{-5}$$

Whakawehe 100 ki te -5.

$$a^{2}-20a=\frac{24000}{-5}$$

Whakawehe 24000 ki te -5.

$$a^{2}-20a=-4800$$

Whakawehea te -20, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -10. Nā, tāpiria te pūrua o te -10 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}-20a+\left(-10\right)^{2}=-4800+\left(-10\right)^{2}$$

Pūrua -10.

$$a^{2}-20a+100=-4800+100$$

Tāpiri -4800 ki te 100.

$$a^{2}-20a+100=-4700$$

Tauwehea te a^{2}-20a+100. 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}.

$$\left(a-10\right)^{2}=-4700$$

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

$$\sqrt{\left(a-10\right)^{2}}=\sqrt{-4700}$$

Whakarūnātia.

$$a-10=10\sqrt{47}i a-10=-10\sqrt{47}i$$

Me tāpiri 10 ki ngā taha e rua o te whārite.

$$a=10+10\sqrt{47}i a=-10\sqrt{47}i+10$$