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

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

Whakaoti mō x

$$x=2\sqrt{2}+2\approx 4.828427125$$

$$x=2-2\sqrt{2}\approx -0.828427125$$

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. Me whakarea ngā taha e rua o te whārite ki te 4x, arā, te tauraro pātahi he tino iti rawa te kitea o 4,2x.

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

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

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

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

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

Tangohia te 2x mai i ngā taha e rua.

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

Pahekotia te -2x me -2x, ka -4x.

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

Tangohia te 4 mai i ngā taha e rua.

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

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

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

Pūrua -4.

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

Whakareatia -4 ki te -4.

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

Tāpiri 16 ki te 16.

$$x=\frac{-\left(-4\right)±\sqrt{32}}{2}$$

Tuhia te pūtakerua o te 32.

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

Ko te tauaro o -4 ko 4.

$$x=\frac{4±4\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{4±4\sqrt{2}}{2} ina he tāpiri te ±. Tāpiri 4 ki te 4\sqrt{2}.

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

Whakawehe 4+4\sqrt{2} ki te 2.

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

Nā, me whakaoti te whārite x=\frac{4±4\sqrt{2}}{2} ina he tango te ±. Tango 4\sqrt{2} mai i 4.

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

Whakawehe 4-4\sqrt{2} ki te 2.

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

Kua oti te whārite te whakatau.

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

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. Me whakarea ngā taha e rua o te whārite ki te 4x, arā, te tauraro pātahi he tino iti rawa te kitea o 4,2x.

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

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

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

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

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

Tangohia te 2x mai i ngā taha e rua.

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

Pahekotia te -2x me -2x, ka -4x.

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

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

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

Pūrua -2.

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

Tāpiri 4 ki te 4.

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

Tauwehea x^{2}-4x+4. 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}.

$$\left(x-2\right)^{2}=8$$

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

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{8}$$

Whakarūnātia.

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

Me tāpiri 2 ki ngā taha e rua o te whārite.

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