Whakaoti i te x-56+64/x=0

$$x-56+ \frac{ 64 }{ x } =0$$

Whakaoti mō x

$$x=12\sqrt{5}+28\approx 54.83281573$$

$$x=28-12\sqrt{5}\approx 1.16718427$$

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.

$$xx+x\left(-56\right)+64=0$$

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

$$x^{2}+x\left(-56\right)+64=0$$

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.

$$x^{2}-56x+64=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -56 mō b, me 64 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-56\right)±\sqrt{\left(-56\right)^{2}-4\times 64}}{2}$$

Pūrua -56.

$$x=\frac{-\left(-56\right)±\sqrt{3136-4\times 64}}{2}$$

Whakareatia -4 ki te 64.

$$x=\frac{-\left(-56\right)±\sqrt{3136-256}}{2}$$

Tāpiri 3136 ki te -256.

$$x=\frac{-\left(-56\right)±\sqrt{2880}}{2}$$

Tuhia te pūtakerua o te 2880.

$$x=\frac{-\left(-56\right)±24\sqrt{5}}{2}$$

Ko te tauaro o -56 ko 56.

$$x=\frac{56±24\sqrt{5}}{2}$$

Nā, me whakaoti te whārite x=\frac{56±24\sqrt{5}}{2} ina he tāpiri te ±. Tāpiri 56 ki te 24\sqrt{5}.

$$x=\frac{24\sqrt{5}+56}{2}$$

Whakawehe 56+24\sqrt{5} ki te 2.

$$x=12\sqrt{5}+28$$

Nā, me whakaoti te whārite x=\frac{56±24\sqrt{5}}{2} ina he tango te ±. Tango 24\sqrt{5} mai i 56.

$$x=\frac{56-24\sqrt{5}}{2}$$

Whakawehe 56-24\sqrt{5} ki te 2.

$$x=28-12\sqrt{5}$$

Kua oti te whārite te whakatau.

$$x=12\sqrt{5}+28 x=28-12\sqrt{5}$$

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.

$$xx+x\left(-56\right)+64=0$$

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

$$x^{2}+x\left(-56\right)+64=0$$

Tangohia te 64 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}+x\left(-56\right)=-64$$

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.

$$x^{2}-56x=-64$$

Whakawehea te -56, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -28. Nā, tāpiria te pūrua o te -28 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-56x+\left(-28\right)^{2}=-64+\left(-28\right)^{2}$$

Pūrua -28.

$$x^{2}-56x+784=-64+784$$

Tāpiri -64 ki te 784.

$$x^{2}-56x+784=720$$

Tauwehea x^{2}-56x+784. 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}.

$$\left(x-28\right)^{2}=720$$

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

$$\sqrt{\left(x-28\right)^{2}}=\sqrt{720}$$

Whakarūnātia.

$$x-28=12\sqrt{5} x-28=-12\sqrt{5}$$

Me tāpiri 28 ki ngā taha e rua o te whārite.

$$x=12\sqrt{5}+28 x=28-12\sqrt{5}$$