Whakaoti i te x-2/2=4x/x-2

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

Whakaoti mō x

$$x=4\sqrt{2}+6\approx 11.656854249$$

$$x=6-4\sqrt{2}\approx 0.343145751$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$\left(x-2\right)\left(x-2\right)=2\times 4x$$

Whakareatia te x-2 ki te x-2, ka \left(x-2\right)^{2}.

$$\left(x-2\right)^{2}=2\times 4x$$

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

$$x^{2}-4x+4=2\times 4x$$

Whakareatia te 2 ki te 4, ka 8.

$$x^{2}-4x+4=8x$$

Tangohia te 8x mai i ngā taha e rua.

$$x^{2}-4x+4-8x=0$$

Pahekotia te -4x me -8x, ka -12x.

$$x^{2}-12x+4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -12 mō b, me 4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 4}}{2}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 4}}{2}$$

Whakareatia -4 ki te 4.

$$x=\frac{-\left(-12\right)±\sqrt{144-16}}{2}$$

Tāpiri 144 ki te -16.

$$x=\frac{-\left(-12\right)±\sqrt{128}}{2}$$

Tuhia te pūtakerua o te 128.

$$x=\frac{-\left(-12\right)±8\sqrt{2}}{2}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±8\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{12±8\sqrt{2}}{2} ina he tāpiri te ±. Tāpiri 12 ki te 8\sqrt{2}.

$$x=\frac{8\sqrt{2}+12}{2}$$

Whakawehe 12+8\sqrt{2} ki te 2.

$$x=4\sqrt{2}+6$$

Nā, me whakaoti te whārite x=\frac{12±8\sqrt{2}}{2} ina he tango te ±. Tango 8\sqrt{2} mai i 12.

$$x=\frac{12-8\sqrt{2}}{2}$$

Whakawehe 12-8\sqrt{2} ki te 2.

$$x=6-4\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=4\sqrt{2}+6 x=6-4\sqrt{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$\left(x-2\right)\left(x-2\right)=2\times 4x$$

Whakareatia te x-2 ki te x-2, ka \left(x-2\right)^{2}.

$$\left(x-2\right)^{2}=2\times 4x$$

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

$$x^{2}-4x+4=2\times 4x$$

Whakareatia te 2 ki te 4, ka 8.

$$x^{2}-4x+4=8x$$

Tangohia te 8x mai i ngā taha e rua.

$$x^{2}-4x+4-8x=0$$

Pahekotia te -4x me -8x, ka -12x.

$$x^{2}-12x+4=0$$

Tangohia te 4 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-12x=-4$$

Whakawehea te -12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -6. Nā, tāpiria te pūrua o te -6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-12x+\left(-6\right)^{2}=-4+\left(-6\right)^{2}$$

Pūrua -6.

$$x^{2}-12x+36=-4+36$$

Tāpiri -4 ki te 36.

$$x^{2}-12x+36=32$$

Tauwehea x^{2}-12x+36. 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}.

$$\left(x-6\right)^{2}=32$$

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

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{32}$$

Whakarūnātia.

$$x-6=4\sqrt{2} x-6=-4\sqrt{2}$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$x=4\sqrt{2}+6 x=6-4\sqrt{2}$$