Whakaoti i te x-17/x^2+2=-6

$$\frac { x - 17 } { x ^ { 2 } + 2 } = - 6$$

Whakaoti mō x

$$x=-1$$

$$x=\frac{5}{6}\approx 0.833333333$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakareatia ngā taha e rua o te whārite ki te x^{2}+2.

$$x-17=-6\left(x^{2}+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -6 ki te x^{2}+2.

$$x-17=-6x^{2}-12$$

Me tāpiri te 6x^{2} ki ngā taha e rua.

$$x-17+6x^{2}=-12$$

Me tāpiri te 12 ki ngā taha e rua.

$$x-17+6x^{2}+12=0$$

Tāpirihia te -17 ki te 12, ka -5.

$$x-5+6x^{2}=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$6x^{2}+x-5=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 6x^{2}+ax+bx-5. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=6\left(-5\right)=-30$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -30.

$$-1,30 -2,15 -3,10 -5,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+30=29 -2+15=13 -3+10=7 -5+6=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=-5 b=6$$

Tuhia anō te 6x^{2}+x-5 hei \left(6x^{2}-5x\right)+\left(6x-5\right).

$$\left(6x^{2}-5x\right)+\left(6x-5\right)$$

Whakatauwehea atu x i te 6x^{2}-5x.

$$x\left(6x-5\right)+6x-5$$

Whakatauwehea atu te kīanga pātahi 6x-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(6x-5\right)\left(x+1\right)$$

Hei kimi otinga whārite, me whakaoti te 6x-5=0 me te x+1=0.

$$x=\frac{5}{6} x=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te x^{2}+2.

$$x-17=-6\left(x^{2}+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -6 ki te x^{2}+2.

$$x-17=-6x^{2}-12$$

Me tāpiri te 6x^{2} ki ngā taha e rua.

$$x-17+6x^{2}=-12$$

Me tāpiri te 12 ki ngā taha e rua.

$$x-17+6x^{2}+12=0$$

Tāpirihia te -17 ki te 12, ka -5.

$$x-5+6x^{2}=0$$

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.

$$6x^{2}+x-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 1 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\times 6\left(-5\right)}}{2\times 6}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\times 6\left(-5\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-1±\sqrt{1-24\left(-5\right)}}{2\times 6}$$

Whakareatia -24 ki te -5.

$$x=\frac{-1±\sqrt{1+120}}{2\times 6}$$

Tāpiri 1 ki te 120.

$$x=\frac{-1±\sqrt{121}}{2\times 6}$$

Tuhia te pūtakerua o te 121.

$$x=\frac{-1±11}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-1±11}{12}$$

Nā, me whakaoti te whārite x=\frac{-1±11}{12} ina he tāpiri te ±. Tāpiri -1 ki te 11.

$$x=\frac{10}{12}$$

Whakahekea te hautanga \frac{10}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{5}{6}$$

Nā, me whakaoti te whārite x=\frac{-1±11}{12} ina he tango te ±. Tango 11 mai i -1.

$$x=-\frac{12}{12}$$

Whakawehe -12 ki te 12.

$$x=-1$$

Kua oti te whārite te whakatau.

$$x=\frac{5}{6} x=-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te x^{2}+2.

$$x-17=-6\left(x^{2}+2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -6 ki te x^{2}+2.

$$x-17=-6x^{2}-12$$

Me tāpiri te 6x^{2} ki ngā taha e rua.

$$x-17+6x^{2}=-12$$

Me tāpiri te 17 ki ngā taha e rua.

$$x+6x^{2}=-12+17$$

Tāpirihia te -12 ki te 17, ka 5.

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

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.

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

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}+x}{6}=\frac{5}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$x^{2}+\frac{1}{6}x=\frac{5}{6}$$

Whakawehea te \frac{1}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{12}. Nā, tāpiria te pūrua o te \frac{1}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{1}{6}x+\left(\frac{1}{12}\right)^{2}=\frac{5}{6}+\left(\frac{1}{12}\right)^{2}$$

Pūruatia \frac{1}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{1}{6}x+\frac{1}{144}=\frac{5}{6}+\frac{1}{144}$$

Tāpiri \frac{5}{6} ki te \frac{1}{144} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}+\frac{1}{6}x+\frac{1}{144}=\frac{121}{144}$$

Tauwehea x^{2}+\frac{1}{6}x+\frac{1}{144}. 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}.

$$\left(x+\frac{1}{12}\right)^{2}=\frac{121}{144}$$

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

$$\sqrt{\left(x+\frac{1}{12}\right)^{2}}=\sqrt{\frac{121}{144}}$$

Whakarūnātia.

$$x+\frac{1}{12}=\frac{11}{12} x+\frac{1}{12}=-\frac{11}{12}$$

Me tango \frac{1}{12} mai i ngā taha e rua o te whārite.

$$x=\frac{5}{6} x=-1$$