Whakaoti i te x+2x+2/x=14000

$$x + 2 x + \frac { 2 } { x } = 14000$$

Whakaoti mō x

$$x = \frac{\sqrt{48999994} + 7000}{3} \approx 4666.66652381$$

$$x=\frac{7000-\sqrt{48999994}}{3}\approx 0.000142857$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$xx+2xx+2=14000x$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+2xx+2=14000x$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+2x^{2}+2=14000x$$

Pahekotia te x^{2} me 2x^{2}, ka 3x^{2}.

$$3x^{2}+2=14000x$$

Tangohia te 14000x mai i ngā taha e rua.

$$3x^{2}+2-14000x=0$$

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.

$$3x^{2}-14000x+2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -14000 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-14000\right)±\sqrt{\left(-14000\right)^{2}-4\times 3\times 2}}{2\times 3}$$

Pūrua -14000.

$$x=\frac{-\left(-14000\right)±\sqrt{196000000-4\times 3\times 2}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-14000\right)±\sqrt{196000000-12\times 2}}{2\times 3}$$

Whakareatia -12 ki te 2.

$$x=\frac{-\left(-14000\right)±\sqrt{196000000-24}}{2\times 3}$$

Tāpiri 196000000 ki te -24.

$$x=\frac{-\left(-14000\right)±\sqrt{195999976}}{2\times 3}$$

Tuhia te pūtakerua o te 195999976.

$$x=\frac{-\left(-14000\right)±2\sqrt{48999994}}{2\times 3}$$

Ko te tauaro o -14000 ko 14000.

$$x=\frac{14000±2\sqrt{48999994}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{14000±2\sqrt{48999994}}{6}$$

Nā, me whakaoti te whārite x=\frac{14000±2\sqrt{48999994}}{6} ina he tāpiri te ±. Tāpiri 14000 ki te 2\sqrt{48999994}.

$$x=\frac{2\sqrt{48999994}+14000}{6}$$

Whakawehe 14000+2\sqrt{48999994} ki te 6.

$$x=\frac{\sqrt{48999994}+7000}{3}$$

Nā, me whakaoti te whārite x=\frac{14000±2\sqrt{48999994}}{6} ina he tango te ±. Tango 2\sqrt{48999994} mai i 14000.

$$x=\frac{14000-2\sqrt{48999994}}{6}$$

Whakawehe 14000-2\sqrt{48999994} ki te 6.

$$x=\frac{7000-\sqrt{48999994}}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{48999994}+7000}{3} x=\frac{7000-\sqrt{48999994}}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$xx+2xx+2=14000x$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+2xx+2=14000x$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+2x^{2}+2=14000x$$

Pahekotia te x^{2} me 2x^{2}, ka 3x^{2}.

$$3x^{2}+2=14000x$$

Tangohia te 14000x mai i ngā taha e rua.

$$3x^{2}+2-14000x=0$$

Tangohia te 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$3x^{2}-14000x=-2$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}-14000x}{3}=-\frac{2}{3}$$

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

$$x^{2}-\frac{14000}{3}x=-\frac{2}{3}$$

Whakawehea te -\frac{14000}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7000}{3}. Nā, tāpiria te pūrua o te -\frac{7000}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{14000}{3}x+\left(-\frac{7000}{3}\right)^{2}=-\frac{2}{3}+\left(-\frac{7000}{3}\right)^{2}$$

Pūruatia -\frac{7000}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{14000}{3}x+\frac{49000000}{9}=-\frac{2}{3}+\frac{49000000}{9}$$

Tāpiri -\frac{2}{3} ki te \frac{49000000}{9} 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.

$$x^{2}-\frac{14000}{3}x+\frac{49000000}{9}=\frac{48999994}{9}$$

Tauwehea te x^{2}-\frac{14000}{3}x+\frac{49000000}{9}. 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}.

$$\left(x-\frac{7000}{3}\right)^{2}=\frac{48999994}{9}$$

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

$$\sqrt{\left(x-\frac{7000}{3}\right)^{2}}=\sqrt{\frac{48999994}{9}}$$

Whakarūnātia.

$$x-\frac{7000}{3}=\frac{\sqrt{48999994}}{3} x-\frac{7000}{3}=-\frac{\sqrt{48999994}}{3}$$

Me tāpiri \frac{7000}{3} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{48999994}+7000}{3} x=\frac{7000-\sqrt{48999994}}{3}$$