Whakaoti i te x=4+2xdiv(1+2x)

$$x=4+2x \div (1+2x)$$

Whakaoti mō x

$$x = \frac{\sqrt{113} + 9}{4} \approx 4.907536453$$

$$x=\frac{9-\sqrt{113}}{4}\approx -0.407536453$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 4 ki te \frac{1+2x}{1+2x}.

$$x=\frac{4\left(1+2x\right)}{1+2x}+\frac{2x}{1+2x}$$

Tā te mea he rite te tauraro o \frac{4\left(1+2x\right)}{1+2x} me \frac{2x}{1+2x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$x=\frac{4\left(1+2x\right)+2x}{1+2x}$$

Mahia ngā whakarea i roto o 4\left(1+2x\right)+2x.

$$x=\frac{4+8x+2x}{1+2x}$$

Whakakotahitia ngā kupu rite i 4+8x+2x.

$$x=\frac{4+10x}{1+2x}$$

Tangohia te \frac{4+10x}{1+2x} mai i ngā taha e rua.

$$x-\frac{4+10x}{1+2x}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{1+2x}{1+2x}.

$$\frac{x\left(1+2x\right)}{1+2x}-\frac{4+10x}{1+2x}=0$$

Tā te mea he rite te tauraro o \frac{x\left(1+2x\right)}{1+2x} me \frac{4+10x}{1+2x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x\left(1+2x\right)-\left(4+10x\right)}{1+2x}=0$$

Mahia ngā whakarea i roto o x\left(1+2x\right)-\left(4+10x\right).

$$\frac{x+2x^{2}-4-10x}{1+2x}=0$$

Whakakotahitia ngā kupu rite i x+2x^{2}-4-10x.

$$\frac{-9x+2x^{2}-4}{1+2x}=0$$

Tē taea kia ōrite te tāupe x ki -\frac{1}{2} nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 2x+1.

$$-9x+2x^{2}-4=0$$

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.

$$2x^{2}-9x-4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -9 mō b, me -4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 2\left(-4\right)}}{2\times 2}$$

Pūrua -9.

$$x=\frac{-\left(-9\right)±\sqrt{81-4\times 2\left(-4\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-9\right)±\sqrt{81-8\left(-4\right)}}{2\times 2}$$

Whakareatia -8 ki te -4.

$$x=\frac{-\left(-9\right)±\sqrt{81+32}}{2\times 2}$$

Tāpiri 81 ki te 32.

$$x=\frac{-\left(-9\right)±\sqrt{113}}{2\times 2}$$

Ko te tauaro o -9 ko 9.

$$x=\frac{9±\sqrt{113}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{9±\sqrt{113}}{4}$$

Nā, me whakaoti te whārite x=\frac{9±\sqrt{113}}{4} ina he tāpiri te ±. Tāpiri 9 ki te \sqrt{113}.

$$x=\frac{\sqrt{113}+9}{4}$$

Nā, me whakaoti te whārite x=\frac{9±\sqrt{113}}{4} ina he tango te ±. Tango \sqrt{113} mai i 9.

$$x=\frac{9-\sqrt{113}}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{113}+9}{4} x=\frac{9-\sqrt{113}}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 4 ki te \frac{1+2x}{1+2x}.

$$x=\frac{4\left(1+2x\right)}{1+2x}+\frac{2x}{1+2x}$$

Tā te mea he rite te tauraro o \frac{4\left(1+2x\right)}{1+2x} me \frac{2x}{1+2x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$x=\frac{4\left(1+2x\right)+2x}{1+2x}$$

Mahia ngā whakarea i roto o 4\left(1+2x\right)+2x.

$$x=\frac{4+8x+2x}{1+2x}$$

Whakakotahitia ngā kupu rite i 4+8x+2x.

$$x=\frac{4+10x}{1+2x}$$

Tangohia te \frac{4+10x}{1+2x} mai i ngā taha e rua.

$$x-\frac{4+10x}{1+2x}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{1+2x}{1+2x}.

$$\frac{x\left(1+2x\right)}{1+2x}-\frac{4+10x}{1+2x}=0$$

Tā te mea he rite te tauraro o \frac{x\left(1+2x\right)}{1+2x} me \frac{4+10x}{1+2x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x\left(1+2x\right)-\left(4+10x\right)}{1+2x}=0$$

Mahia ngā whakarea i roto o x\left(1+2x\right)-\left(4+10x\right).

$$\frac{x+2x^{2}-4-10x}{1+2x}=0$$

Whakakotahitia ngā kupu rite i x+2x^{2}-4-10x.

$$\frac{-9x+2x^{2}-4}{1+2x}=0$$

Tē taea kia ōrite te tāupe x ki -\frac{1}{2} nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 2x+1.

$$-9x+2x^{2}-4=0$$

Me tāpiri te 4 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$-9x+2x^{2}=4$$

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.

$$2x^{2}-9x=4$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-9x}{2}=\frac{4}{2}$$

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

$$x^{2}-\frac{9}{2}x=\frac{4}{2}$$

Whakawehe 4 ki te 2.

$$x^{2}-\frac{9}{2}x=2$$

Whakawehea te -\frac{9}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{4}. Nā, tāpiria te pūrua o te -\frac{9}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{9}{2}x+\left(-\frac{9}{4}\right)^{2}=2+\left(-\frac{9}{4}\right)^{2}$$

Pūruatia -\frac{9}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{9}{2}x+\frac{81}{16}=2+\frac{81}{16}$$

Tāpiri 2 ki te \frac{81}{16}.

$$x^{2}-\frac{9}{2}x+\frac{81}{16}=\frac{113}{16}$$

Tauwehea x^{2}-\frac{9}{2}x+\frac{81}{16}. 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}.

$$\left(x-\frac{9}{4}\right)^{2}=\frac{113}{16}$$

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

$$\sqrt{\left(x-\frac{9}{4}\right)^{2}}=\sqrt{\frac{113}{16}}$$

Whakarūnātia.

$$x-\frac{9}{4}=\frac{\sqrt{113}}{4} x-\frac{9}{4}=-\frac{\sqrt{113}}{4}$$

Me tāpiri \frac{9}{4} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{113}+9}{4} x=\frac{9-\sqrt{113}}{4}$$