Whakaoti i te 2x(4-x)div2=2

$$2x(4-x) \div 2=2$$

Whakaoti mō x

$$x=\sqrt{2}+2\approx 3.414213562$$

$$x=2-\sqrt{2}\approx 0.585786438$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua ki te 2.

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

Me whakakore te 2 ki ngā taha e rua.

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

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 4-x.

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

Tangohia te 2 mai i ngā taha e rua.

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

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.

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

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

$$x=\frac{-4±\sqrt{4^{2}-4\left(-1\right)\left(-2\right)}}{2\left(-1\right)}$$

Pūrua 4.

$$x=\frac{-4±\sqrt{16-4\left(-1\right)\left(-2\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-4±\sqrt{16+4\left(-2\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -2.

$$x=\frac{-4±\sqrt{16-8}}{2\left(-1\right)}$$

Tāpiri 16 ki te -8.

$$x=\frac{-4±\sqrt{8}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 8.

$$x=\frac{-4±2\sqrt{2}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-4±2\sqrt{2}}{-2}$$

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

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

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

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

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

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

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

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

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Me whakarea ngā taha e rua ki te 2.

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

Me whakakore te 2 ki ngā taha e rua.

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

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 4-x.

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

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.

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

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+4x}{-1}=\frac{2}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{4}{-1}x=\frac{2}{-1}$$

Whakawehe 4 ki te -1.

$$x^{2}-4x=\frac{2}{-1}$$

Whakawehe 2 ki te -1.

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

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.

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

Pūrua -2.

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

Tāpiri -2 ki te 4.

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

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}.

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

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

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

Whakarūnātia.

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

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

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