Whakaoti i te V^2=25^2+(75-2V)^2

$$V ^ { 2 } = 25 ^ { 2 } + ( 75 - 2 V ) ^ { 2 }$$

Whakaoti mō V

$$V=\frac{25\sqrt{6}}{3}+50\approx 70.412414523$$

$$V=-\frac{25\sqrt{6}}{3}+50\approx 29.587585477$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 25 mā te pū o 2, kia riro ko 625.

$$V^{2}=625+\left(75-2V\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(75-2V\right)^{2}.

$$V^{2}=625+5625-300V+4V^{2}$$

Tāpirihia te 625 ki te 5625, ka 6250.

$$V^{2}=6250-300V+4V^{2}$$

Tangohia te 6250 mai i ngā taha e rua.

$$V^{2}-6250=-300V+4V^{2}$$

Me tāpiri te 300V ki ngā taha e rua.

$$V^{2}-6250+300V=4V^{2}$$

Tangohia te 4V^{2} mai i ngā taha e rua.

$$V^{2}-6250+300V-4V^{2}=0$$

Pahekotia te V^{2} me -4V^{2}, ka -3V^{2}.

$$-3V^{2}-6250+300V=0$$

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.

$$-3V^{2}+300V-6250=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, 300 mō b, me -6250 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$V=\frac{-300±\sqrt{300^{2}-4\left(-3\right)\left(-6250\right)}}{2\left(-3\right)}$$

Pūrua 300.

$$V=\frac{-300±\sqrt{90000-4\left(-3\right)\left(-6250\right)}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$V=\frac{-300±\sqrt{90000+12\left(-6250\right)}}{2\left(-3\right)}$$

Whakareatia 12 ki te -6250.

$$V=\frac{-300±\sqrt{90000-75000}}{2\left(-3\right)}$$

Tāpiri 90000 ki te -75000.

$$V=\frac{-300±\sqrt{15000}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 15000.

$$V=\frac{-300±50\sqrt{6}}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$V=\frac{-300±50\sqrt{6}}{-6}$$

Nā, me whakaoti te whārite V=\frac{-300±50\sqrt{6}}{-6} ina he tāpiri te ±. Tāpiri -300 ki te 50\sqrt{6}.

$$V=\frac{50\sqrt{6}-300}{-6}$$

Whakawehe -300+50\sqrt{6} ki te -6.

$$V=-\frac{25\sqrt{6}}{3}+50$$

Nā, me whakaoti te whārite V=\frac{-300±50\sqrt{6}}{-6} ina he tango te ±. Tango 50\sqrt{6} mai i -300.

$$V=\frac{-50\sqrt{6}-300}{-6}$$

Whakawehe -300-50\sqrt{6} ki te -6.

$$V=\frac{25\sqrt{6}}{3}+50$$

Kua oti te whārite te whakatau.

$$V=-\frac{25\sqrt{6}}{3}+50 V=\frac{25\sqrt{6}}{3}+50$$

Ngā Upane mō te Whakaoti i te Pūrua

Tātaihia te 25 mā te pū o 2, kia riro ko 625.

$$V^{2}=625+\left(75-2V\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(75-2V\right)^{2}.

$$V^{2}=625+5625-300V+4V^{2}$$

Tāpirihia te 625 ki te 5625, ka 6250.

$$V^{2}=6250-300V+4V^{2}$$

Me tāpiri te 300V ki ngā taha e rua.

$$V^{2}+300V=6250+4V^{2}$$

Tangohia te 4V^{2} mai i ngā taha e rua.

$$V^{2}+300V-4V^{2}=6250$$

Pahekotia te V^{2} me -4V^{2}, ka -3V^{2}.

$$-3V^{2}+300V=6250$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3V^{2}+300V}{-3}=\frac{6250}{-3}$$

Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.

$$V^{2}+\frac{300}{-3}V=\frac{6250}{-3}$$

Whakawehe 300 ki te -3.

$$V^{2}-100V=\frac{6250}{-3}$$

Whakawehe 6250 ki te -3.

$$V^{2}-100V=-\frac{6250}{3}$$

Whakawehea te -100, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -50. Nā, tāpiria te pūrua o te -50 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$V^{2}-100V+\left(-50\right)^{2}=-\frac{6250}{3}+\left(-50\right)^{2}$$

Pūrua -50.

$$V^{2}-100V+2500=-\frac{6250}{3}+2500$$

Tāpiri -\frac{6250}{3} ki te 2500.

$$V^{2}-100V+2500=\frac{1250}{3}$$

Tauwehea V^{2}-100V+2500. 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}.

$$\left(V-50\right)^{2}=\frac{1250}{3}$$

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

$$\sqrt{\left(V-50\right)^{2}}=\sqrt{\frac{1250}{3}}$$

Whakarūnātia.

$$V-50=\frac{25\sqrt{6}}{3} V-50=-\frac{25\sqrt{6}}{3}$$

Me tāpiri 50 ki ngā taha e rua o te whārite.

$$V=\frac{25\sqrt{6}}{3}+50 V=-\frac{25\sqrt{6}}{3}+50$$