Whakaoti i te 6x/x+1=6-x/6

$$\frac { 6 x } { x + 1 } = \frac { 6 - x } { 6 }$$

Whakaoti mō x

$$x=\frac{\sqrt{985}-31}{2}\approx 0.192354826$$

$$x=\frac{-\sqrt{985}-31}{2}\approx -31.192354826$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki -1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 6\left(x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+1,6.

$$6\times 6x=\left(x+1\right)\left(6-x\right)$$

Whakareatia te 6 ki te 6, ka 36.

$$36x=\left(x+1\right)\left(6-x\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+1 ki te 6-x ka whakakotahi i ngā kupu rite.

$$36x=5x-x^{2}+6$$

Tangohia te 5x mai i ngā taha e rua.

$$36x-5x=-x^{2}+6$$

Pahekotia te 36x me -5x, ka 31x.

$$31x=-x^{2}+6$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$31x+x^{2}=6$$

Tangohia te 6 mai i ngā taha e rua.

$$31x+x^{2}-6=0$$

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.

$$x^{2}+31x-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 31 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-31±\sqrt{31^{2}-4\left(-6\right)}}{2}$$

Pūrua 31.

$$x=\frac{-31±\sqrt{961-4\left(-6\right)}}{2}$$

Whakareatia -4 ki te -6.

$$x=\frac{-31±\sqrt{961+24}}{2}$$

Tāpiri 961 ki te 24.

$$x=\frac{-31±\sqrt{985}}{2}$$

Nā, me whakaoti te whārite x=\frac{-31±\sqrt{985}}{2} ina he tāpiri te ±. Tāpiri -31 ki te \sqrt{985}.

$$x=\frac{\sqrt{985}-31}{2}$$

Nā, me whakaoti te whārite x=\frac{-31±\sqrt{985}}{2} ina he tango te ±. Tango \sqrt{985} mai i -31.

$$x=\frac{-\sqrt{985}-31}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{985}-31}{2} x=\frac{-\sqrt{985}-31}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki -1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 6\left(x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+1,6.

$$6\times 6x=\left(x+1\right)\left(6-x\right)$$

Whakareatia te 6 ki te 6, ka 36.

$$36x=\left(x+1\right)\left(6-x\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+1 ki te 6-x ka whakakotahi i ngā kupu rite.

$$36x=5x-x^{2}+6$$

Tangohia te 5x mai i ngā taha e rua.

$$36x-5x=-x^{2}+6$$

Pahekotia te 36x me -5x, ka 31x.

$$31x=-x^{2}+6$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$31x+x^{2}=6$$

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.

$$x^{2}+31x=6$$

Whakawehea te 31, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{31}{2}. Nā, tāpiria te pūrua o te \frac{31}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+31x+\left(\frac{31}{2}\right)^{2}=6+\left(\frac{31}{2}\right)^{2}$$

Pūruatia \frac{31}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+31x+\frac{961}{4}=6+\frac{961}{4}$$

Tāpiri 6 ki te \frac{961}{4}.

$$x^{2}+31x+\frac{961}{4}=\frac{985}{4}$$

Tauwehea x^{2}+31x+\frac{961}{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}.

$$\left(x+\frac{31}{2}\right)^{2}=\frac{985}{4}$$

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

$$\sqrt{\left(x+\frac{31}{2}\right)^{2}}=\sqrt{\frac{985}{4}}$$

Whakarūnātia.

$$x+\frac{31}{2}=\frac{\sqrt{985}}{2} x+\frac{31}{2}=-\frac{\sqrt{985}}{2}$$

Me tango \frac{31}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{985}-31}{2} x=\frac{-\sqrt{985}-31}{2}$$