Whakaoti i te (x^2+6)(7-x^2)-36=x^4+12x^2

$$( x ^ { 2 } + 6 ) ( 7 - x ^ { 2 } ) - 36 = x ^ { 4 } + 12 x ^ { 2 }$$

Whakaoti mō x (complex solution)

$$x=\sqrt{6}i\approx 2.449489743i$$

$$x=-\sqrt{6}i\approx -0-2.449489743i$$

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x^{2}+6 ki te 7-x^{2} ka whakakotahi i ngā kupu rite.

$$x^{2}-x^{4}+42-36=x^{4}+12x^{2}$$

Tangohia te 36 i te 42, ka 6.

$$x^{2}-x^{4}+6=x^{4}+12x^{2}$$

Tangohia te x^{4} mai i ngā taha e rua.

$$x^{2}-x^{4}+6-x^{4}=12x^{2}$$

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

$$x^{2}-2x^{4}+6=12x^{2}$$

Tangohia te 12x^{2} mai i ngā taha e rua.

$$x^{2}-2x^{4}+6-12x^{2}=0$$

Pahekotia te x^{2} me -12x^{2}, ka -11x^{2}.

$$-11x^{2}-2x^{4}+6=0$$

Whakakapia te t mō te x^{2}.

$$-2t^{2}-11t+6=0$$

Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te -2 mō te a, te -11 mō te b, me te 6 mō te c i te ture pūrua.

$$t=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\left(-2\right)\times 6}}{-2\times 2}$$

Mahia ngā tātaitai.

$$t=\frac{11±13}{-4}$$

Whakaotia te whārite t=\frac{11±13}{-4} ina he tōrunga te ±, ina he tōraro te ±.

$$t=-6 t=\frac{1}{2}$$

I te mea ko x=t^{2}, ka riro ngā otinga mā te arotake i te x=±\sqrt{t} mō ia t.

$$x=-\sqrt{6}i x=\sqrt{6}i x=-\frac{\sqrt{2}}{2} x=\frac{\sqrt{2}}{2}$$

Whakaoti mō x

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x^{2}+6 ki te 7-x^{2} ka whakakotahi i ngā kupu rite.

$$x^{2}-x^{4}+42-36=x^{4}+12x^{2}$$

Tangohia te 36 i te 42, ka 6.

$$x^{2}-x^{4}+6=x^{4}+12x^{2}$$

Tangohia te x^{4} mai i ngā taha e rua.

$$x^{2}-x^{4}+6-x^{4}=12x^{2}$$

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

$$x^{2}-2x^{4}+6=12x^{2}$$

Tangohia te 12x^{2} mai i ngā taha e rua.

$$x^{2}-2x^{4}+6-12x^{2}=0$$

Pahekotia te x^{2} me -12x^{2}, ka -11x^{2}.

$$-11x^{2}-2x^{4}+6=0$$

Whakakapia te t mō te x^{2}.

$$-2t^{2}-11t+6=0$$

Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te -2 mō te a, te -11 mō te b, me te 6 mō te c i te ture pūrua.

$$t=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\left(-2\right)\times 6}}{-2\times 2}$$

Mahia ngā tātaitai.

$$t=\frac{11±13}{-4}$$

Whakaotia te whārite t=\frac{11±13}{-4} ina he tōrunga te ±, ina he tōraro te ±.

$$t=-6 t=\frac{1}{2}$$

I te mea ko x=t^{2}, ka riro ngā otinga mā te arotake i te x=±\sqrt{t} mō t tōrunga.

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