Whakaoti i te (x-1)(x+1)=5(1-3x)(1+3x)+1

$$(x-1)(x+1)=5(1-3x)(1+3x)+1$$

Whakaoti mō x

$$x=\frac{\sqrt{322}}{46}\approx 0.390094749$$

$$x=-\frac{\sqrt{322}}{46}\approx -0.390094749$$

Ngā Upane mā te Kimi Pūtakerua

Whakaarohia te \left(x-1\right)\left(x+1\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 1.

$$x^{2}-1=5\left(1-3x\right)\left(1+3x\right)+1$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te 1-3x.

$$x^{2}-1=\left(5-15x\right)\left(1+3x\right)+1$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 5-15x ki te 1+3x ka whakakotahi i ngā kupu rite.

$$x^{2}-1=5-45x^{2}+1$$

Tāpirihia te 5 ki te 1, ka 6.

$$x^{2}-1=6-45x^{2}$$

Me tāpiri te 45x^{2} ki ngā taha e rua.

$$x^{2}-1+45x^{2}=6$$

Pahekotia te x^{2} me 45x^{2}, ka 46x^{2}.

$$46x^{2}-1=6$$

Me tāpiri te 1 ki ngā taha e rua.

$$46x^{2}=6+1$$

Tāpirihia te 6 ki te 1, ka 7.

$$46x^{2}=7$$

Whakawehea ngā taha e rua ki te 46.

$$x^{2}=\frac{7}{46}$$

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

$$x=\frac{\sqrt{322}}{46} x=-\frac{\sqrt{322}}{46}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakaarohia te \left(x-1\right)\left(x+1\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 1.

$$x^{2}-1=5\left(1-3x\right)\left(1+3x\right)+1$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te 1-3x.

$$x^{2}-1=\left(5-15x\right)\left(1+3x\right)+1$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 5-15x ki te 1+3x ka whakakotahi i ngā kupu rite.

$$x^{2}-1=5-45x^{2}+1$$

Tāpirihia te 5 ki te 1, ka 6.

$$x^{2}-1=6-45x^{2}$$

Tangohia te 6 mai i ngā taha e rua.

$$x^{2}-1-6=-45x^{2}$$

Tangohia te 6 i te -1, ka -7.

$$x^{2}-7=-45x^{2}$$

Me tāpiri te 45x^{2} ki ngā taha e rua.

$$x^{2}-7+45x^{2}=0$$

Pahekotia te x^{2} me 45x^{2}, ka 46x^{2}.

$$46x^{2}-7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 46 mō a, 0 mō b, me -7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 46\left(-7\right)}}{2\times 46}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 46\left(-7\right)}}{2\times 46}$$

Whakareatia -4 ki te 46.

$$x=\frac{0±\sqrt{-184\left(-7\right)}}{2\times 46}$$

Whakareatia -184 ki te -7.

$$x=\frac{0±\sqrt{1288}}{2\times 46}$$

Tuhia te pūtakerua o te 1288.

$$x=\frac{0±2\sqrt{322}}{2\times 46}$$

Whakareatia 2 ki te 46.

$$x=\frac{0±2\sqrt{322}}{92}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{322}}{92} ina he tāpiri te ±.

$$x=\frac{\sqrt{322}}{46}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{322}}{92} ina he tango te ±.

$$x=-\frac{\sqrt{322}}{46}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{322}}{46} x=-\frac{\sqrt{322}}{46}$$