Whakaoti i te (9x+1)(9x-1)=1

$$( 9 x + 1 ) ( 9 x - 1 ) = 1$$

Whakaoti mō x

$$x=\frac{\sqrt{2}}{9}\approx 0.15713484$$

$$x=-\frac{\sqrt{2}}{9}\approx -0.15713484$$

Ngā Upane mā te Kimi Pūtakerua

Whakaarohia te \left(9x+1\right)\left(9x-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.

$$\left(9x\right)^{2}-1=1$$

Whakarohaina te \left(9x\right)^{2}.

$$9^{2}x^{2}-1=1$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$81x^{2}-1=1$$

Me tāpiri te 1 ki ngā taha e rua.

$$81x^{2}=1+1$$

Tāpirihia te 1 ki te 1, ka 2.

$$81x^{2}=2$$

Whakawehea ngā taha e rua ki te 81.

$$x^{2}=\frac{2}{81}$$

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

$$x=\frac{\sqrt{2}}{9} x=-\frac{\sqrt{2}}{9}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakaarohia te \left(9x+1\right)\left(9x-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.

$$\left(9x\right)^{2}-1=1$$

Whakarohaina te \left(9x\right)^{2}.

$$9^{2}x^{2}-1=1$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$81x^{2}-1=1$$

Tangohia te 1 mai i ngā taha e rua.

$$81x^{2}-1-1=0$$

Tangohia te 1 i te -1, ka -2.

$$81x^{2}-2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 81 mō a, 0 mō b, me -2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 81\left(-2\right)}}{2\times 81}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 81\left(-2\right)}}{2\times 81}$$

Whakareatia -4 ki te 81.

$$x=\frac{0±\sqrt{-324\left(-2\right)}}{2\times 81}$$

Whakareatia -324 ki te -2.

$$x=\frac{0±\sqrt{648}}{2\times 81}$$

Tuhia te pūtakerua o te 648.

$$x=\frac{0±18\sqrt{2}}{2\times 81}$$

Whakareatia 2 ki te 81.

$$x=\frac{0±18\sqrt{2}}{162}$$

Nā, me whakaoti te whārite x=\frac{0±18\sqrt{2}}{162} ina he tāpiri te ±.

$$x=\frac{\sqrt{2}}{9}$$

Nā, me whakaoti te whārite x=\frac{0±18\sqrt{2}}{162} ina he tango te ±.

$$x=-\frac{\sqrt{2}}{9}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{2}}{9} x=-\frac{\sqrt{2}}{9}$$