Whakaoti i te 360/x-2-360/x=2

$$\frac{ 360 }{ x-2 } - \frac{ 360 }{ x } = 2$$

Whakaoti mō x

$$x=-18$$

$$x=20$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-2,x.

$$x\times 360-\left(x-2\right)\times 360=2x\left(x-2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te 360.

$$x\times 360-\left(360x-720\right)=2x\left(x-2\right)$$

Hei kimi i te tauaro o 360x-720, kimihia te tauaro o ia taurangi.

$$x\times 360-360x+720=2x\left(x-2\right)$$

Pahekotia te x\times 360 me -360x, ka 0.

$$720=2x\left(x-2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-2.

$$720=2x^{2}-4x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2x^{2}-4x=720$$

Tangohia te 720 mai i ngā taha e rua.

$$2x^{2}-4x-720=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -4 mō b, me -720 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 2\left(-720\right)}}{2\times 2}$$

Pūrua -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 2\left(-720\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-4\right)±\sqrt{16-8\left(-720\right)}}{2\times 2}$$

Whakareatia -8 ki te -720.

$$x=\frac{-\left(-4\right)±\sqrt{16+5760}}{2\times 2}$$

Tāpiri 16 ki te 5760.

$$x=\frac{-\left(-4\right)±\sqrt{5776}}{2\times 2}$$

Tuhia te pūtakerua o te 5776.

$$x=\frac{-\left(-4\right)±76}{2\times 2}$$

Ko te tauaro o -4 ko 4.

$$x=\frac{4±76}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{4±76}{4}$$

Nā, me whakaoti te whārite x=\frac{4±76}{4} ina he tāpiri te ±. Tāpiri 4 ki te 76.

$$x=\frac{80}{4}$$

Whakawehe 80 ki te 4.

$$x=20$$

Nā, me whakaoti te whārite x=\frac{4±76}{4} ina he tango te ±. Tango 76 mai i 4.

$$x=-\frac{72}{4}$$

Whakawehe -72 ki te 4.

$$x=-18$$

Kua oti te whārite te whakatau.

$$x=20 x=-18$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-2,x.

$$x\times 360-\left(x-2\right)\times 360=2x\left(x-2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te 360.

$$x\times 360-\left(360x-720\right)=2x\left(x-2\right)$$

Hei kimi i te tauaro o 360x-720, kimihia te tauaro o ia taurangi.

$$x\times 360-360x+720=2x\left(x-2\right)$$

Pahekotia te x\times 360 me -360x, ka 0.

$$720=2x\left(x-2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-2.

$$720=2x^{2}-4x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2x^{2}-4x=720$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-4x}{2}=\frac{720}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\left(-\frac{4}{2}\right)x=\frac{720}{2}$$

Whakawehe -4 ki te 2.

$$x^{2}-2x=\frac{720}{2}$$

Whakawehe 720 ki te 2.

$$x^{2}-2x=360$$

Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-2x+1=360+1$$

Tāpiri 360 ki te 1.

$$x^{2}-2x+1=361$$

Tauwehea x^{2}-2x+1. 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}.

$$\left(x-1\right)^{2}=361$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{361}$$

Whakarūnātia.

$$x-1=19 x-1=-19$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=20 x=-18$$