Whakaoti i te 4a^2/1-a=1898

$$\frac { 4 a ^ { 2 } } { 1 - a } = 1898$$

Whakaoti mō a

$$a=\frac{\sqrt{908193}-949}{4}\approx 0.997901355$$

$$a=\frac{-\sqrt{908193}-949}{4}\approx -475.497901355$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe a ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -a+1.

$$4a^{2}=1898\left(-a+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1898 ki te -a+1.

$$4a^{2}=-1898a+1898$$

Me tāpiri te 1898a ki ngā taha e rua.

$$4a^{2}+1898a=1898$$

Tangohia te 1898 mai i ngā taha e rua.

$$4a^{2}+1898a-1898=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 1898 mō b, me -1898 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-1898±\sqrt{1898^{2}-4\times 4\left(-1898\right)}}{2\times 4}$$

Pūrua 1898.

$$a=\frac{-1898±\sqrt{3602404-4\times 4\left(-1898\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$a=\frac{-1898±\sqrt{3602404-16\left(-1898\right)}}{2\times 4}$$

Whakareatia -16 ki te -1898.

$$a=\frac{-1898±\sqrt{3602404+30368}}{2\times 4}$$

Tāpiri 3602404 ki te 30368.

$$a=\frac{-1898±\sqrt{3632772}}{2\times 4}$$

Tuhia te pūtakerua o te 3632772.

$$a=\frac{-1898±2\sqrt{908193}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$a=\frac{-1898±2\sqrt{908193}}{8}$$

Nā, me whakaoti te whārite a=\frac{-1898±2\sqrt{908193}}{8} ina he tāpiri te ±. Tāpiri -1898 ki te 2\sqrt{908193}.

$$a=\frac{2\sqrt{908193}-1898}{8}$$

Whakawehe -1898+2\sqrt{908193} ki te 8.

$$a=\frac{\sqrt{908193}-949}{4}$$

Nā, me whakaoti te whārite a=\frac{-1898±2\sqrt{908193}}{8} ina he tango te ±. Tango 2\sqrt{908193} mai i -1898.

$$a=\frac{-2\sqrt{908193}-1898}{8}$$

Whakawehe -1898-2\sqrt{908193} ki te 8.

$$a=\frac{-\sqrt{908193}-949}{4}$$

Kua oti te whārite te whakatau.

$$a=\frac{\sqrt{908193}-949}{4} a=\frac{-\sqrt{908193}-949}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe a ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -a+1.

$$4a^{2}=1898\left(-a+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1898 ki te -a+1.

$$4a^{2}=-1898a+1898$$

Me tāpiri te 1898a ki ngā taha e rua.

$$4a^{2}+1898a=1898$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4a^{2}+1898a}{4}=\frac{1898}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$a^{2}+\frac{1898}{4}a=\frac{1898}{4}$$

Whakahekea te hautanga \frac{1898}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$a^{2}+\frac{949}{2}a=\frac{1898}{4}$$

Whakahekea te hautanga \frac{1898}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$a^{2}+\frac{949}{2}a=\frac{949}{2}$$

Whakawehea te \frac{949}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{949}{4}. Nā, tāpiria te pūrua o te \frac{949}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}+\frac{949}{2}a+\left(\frac{949}{4}\right)^{2}=\frac{949}{2}+\left(\frac{949}{4}\right)^{2}$$

Pūruatia \frac{949}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$a^{2}+\frac{949}{2}a+\frac{900601}{16}=\frac{949}{2}+\frac{900601}{16}$$

Tāpiri \frac{949}{2} ki te \frac{900601}{16} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$a^{2}+\frac{949}{2}a+\frac{900601}{16}=\frac{908193}{16}$$

Tauwehea a^{2}+\frac{949}{2}a+\frac{900601}{16}. 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}.

$$\left(a+\frac{949}{4}\right)^{2}=\frac{908193}{16}$$

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

$$\sqrt{\left(a+\frac{949}{4}\right)^{2}}=\sqrt{\frac{908193}{16}}$$

Whakarūnātia.

$$a+\frac{949}{4}=\frac{\sqrt{908193}}{4} a+\frac{949}{4}=-\frac{\sqrt{908193}}{4}$$

Me tango \frac{949}{4} mai i ngā taha e rua o te whārite.

$$a=\frac{\sqrt{908193}-949}{4} a=\frac{-\sqrt{908193}-949}{4}$$