Whakaoti i te (x-5)(x+5)=2(x-1)(x+1)

$$( x - 5 ) ( x + 5 ) = 2 ( x - 1 ) ( x + 1 )$$

Whakaoti mō x (complex solution)

$$x=-\sqrt{23}i\approx -0-4.795831523i$$

$$x=\sqrt{23}i\approx 4.795831523i$$

Ngā Upane mā te Kimi Pūtakerua

Whakaarohia te \left(x-5\right)\left(x+5\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 5.

$$x^{2}-25=2\left(x-1\right)\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x-1.

$$x^{2}-25=\left(2x-2\right)\left(x+1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-2 ki te x+1 ka whakakotahi i ngā kupu rite.

$$x^{2}-25=2x^{2}-2$$

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

$$x^{2}-25-2x^{2}=-2$$

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

$$-x^{2}-25=-2$$

Me tāpiri te 25 ki ngā taha e rua.

$$-x^{2}=-2+25$$

Tāpirihia te -2 ki te 25, ka 23.

$$-x^{2}=23$$

Whakawehea ngā taha e rua ki te -1.

$$x^{2}=-23$$

Kua oti te whārite te whakatau.

$$x=\sqrt{23}i x=-\sqrt{23}i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakaarohia te \left(x-5\right)\left(x+5\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 5.

$$x^{2}-25=2\left(x-1\right)\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x-1.

$$x^{2}-25=\left(2x-2\right)\left(x+1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-2 ki te x+1 ka whakakotahi i ngā kupu rite.

$$x^{2}-25=2x^{2}-2$$

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

$$x^{2}-25-2x^{2}=-2$$

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

$$-x^{2}-25=-2$$

Me tāpiri te 2 ki ngā taha e rua.

$$-x^{2}-25+2=0$$

Tāpirihia te -25 ki te 2, ka -23.

$$-x^{2}-23=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 0 mō b, me -23 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-23\right)}}{2\left(-1\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-23\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{0±\sqrt{4\left(-23\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -23.

$$x=\frac{0±\sqrt{-92}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te -92.

$$x=\frac{0±2\sqrt{23}i}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{0±2\sqrt{23}i}{-2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{23}i}{-2} ina he tāpiri te ±.

$$x=-\sqrt{23}i$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{23}i}{-2} ina he tango te ±.

$$x=\sqrt{23}i$$

Kua oti te whārite te whakatau.

$$x=-\sqrt{23}i x=\sqrt{23}i$$