Whakaoti i te 3/x^4-1-1/2x^2+2=-1/6-6x^2

$$\frac { 3 } { x ^ { 4 } - 1 } - \frac { 1 } { 2 x ^ { 2 } + 2 } = - \frac { 1 } { 6 - 6 x ^ { 2 } }$$

Whakaoti mō x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -1,1 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)\left(x+1\right)\left(x^{2}+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o x^{4}-1,2x^{2}+2,6-6x^{2}.

$$6\times 3-\left(3x^{2}-3\right)=1+x^{2}$$

Whakareatia te 6 ki te 3, ka 18.

$$18-\left(3x^{2}-3\right)=1+x^{2}$$

Hei kimi i te tauaro o 3x^{2}-3, kimihia te tauaro o ia taurangi.

$$18-3x^{2}+3=1+x^{2}$$

Tāpirihia te 18 ki te 3, ka 21.

$$21-3x^{2}=1+x^{2}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$21-3x^{2}-x^{2}=1$$

Pahekotia te -3x^{2} me -x^{2}, ka -4x^{2}.

$$21-4x^{2}=1$$

Tangohia te 21 mai i ngā taha e rua.

$$-4x^{2}=1-21$$

Tangohia te 21 i te 1, ka -20.

$$-4x^{2}=-20$$

Whakawehea ngā taha e rua ki te -4.

$$x^{2}=\frac{-20}{-4}$$

Whakawehea te -20 ki te -4, kia riro ko 5.

$$x^{2}=5$$

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

$$x=\sqrt{5} x=-\sqrt{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -1,1 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)\left(x+1\right)\left(x^{2}+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o x^{4}-1,2x^{2}+2,6-6x^{2}.

$$6\times 3-\left(3x^{2}-3\right)=1+x^{2}$$

Whakareatia te 6 ki te 3, ka 18.

$$18-\left(3x^{2}-3\right)=1+x^{2}$$

Hei kimi i te tauaro o 3x^{2}-3, kimihia te tauaro o ia taurangi.

$$18-3x^{2}+3=1+x^{2}$$

Tāpirihia te 18 ki te 3, ka 21.

$$21-3x^{2}=1+x^{2}$$

Tangohia te 1 mai i ngā taha e rua.

$$21-3x^{2}-1=x^{2}$$

Tangohia te 1 i te 21, ka 20.

$$20-3x^{2}=x^{2}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$20-3x^{2}-x^{2}=0$$

Pahekotia te -3x^{2} me -x^{2}, ka -4x^{2}.

$$20-4x^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$-4x^{2}+20=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -4 mō a, 0 mō b, me 20 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 20}}{2\left(-4\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)\times 20}}{2\left(-4\right)}$$

Whakareatia -4 ki te -4.

$$x=\frac{0±\sqrt{16\times 20}}{2\left(-4\right)}$$

Whakareatia 16 ki te 20.

$$x=\frac{0±\sqrt{320}}{2\left(-4\right)}$$

Tuhia te pūtakerua o te 320.

$$x=\frac{0±8\sqrt{5}}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{0±8\sqrt{5}}{-8}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{5}}{-8} ina he tāpiri te ±.

$$x=-\sqrt{5}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{5}}{-8} ina he tango te ±.

$$x=\sqrt{5}$$

Kua oti te whārite te whakatau.

$$x=-\sqrt{5} x=\sqrt{5}$$