Whakaoti i te (5x+1)(5x-1)=[1]

$$( 5 x + 1 ) ( 5 x - 1 ) = [ 1 ]$$

Whakaoti mō x

$$x=\frac{\sqrt{2}}{5}\approx 0.282842712$$

$$x=-\frac{\sqrt{2}}{5}\approx -0.282842712$$

Ngā Upane mā te Kimi Pūtakerua

Whakaarohia te \left(5x+1\right)\left(5x-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.

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

Whakarohaina te \left(5x\right)^{2}.

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

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$25x^{2}-1=1$$

Me tāpiri te 1 ki ngā taha e rua.

$$25x^{2}=1+1$$

Tāpirihia te 1 ki te 1, ka 2.

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

Whakawehea ngā taha e rua ki te 25.

$$x^{2}=\frac{2}{25}$$

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

$$x=\frac{\sqrt{2}}{5} x=-\frac{\sqrt{2}}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakaarohia te \left(5x+1\right)\left(5x-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.

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

Whakarohaina te \left(5x\right)^{2}.

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

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$25x^{2}-1=1$$

Tangohia te 1 mai i ngā taha e rua.

$$25x^{2}-1-1=0$$

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

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 25 mō a, 0 mō b, me -2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 25\left(-2\right)}}{2\times 25}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 25\left(-2\right)}}{2\times 25}$$

Whakareatia -4 ki te 25.

$$x=\frac{0±\sqrt{-100\left(-2\right)}}{2\times 25}$$

Whakareatia -100 ki te -2.

$$x=\frac{0±\sqrt{200}}{2\times 25}$$

Tuhia te pūtakerua o te 200.

$$x=\frac{0±10\sqrt{2}}{2\times 25}$$

Whakareatia 2 ki te 25.

$$x=\frac{0±10\sqrt{2}}{50}$$

Nā, me whakaoti te whārite x=\frac{0±10\sqrt{2}}{50} ina he tāpiri te ±.

$$x=\frac{\sqrt{2}}{5}$$

Nā, me whakaoti te whārite x=\frac{0±10\sqrt{2}}{50} ina he tango te ±.

$$x=-\frac{\sqrt{2}}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{2}}{5} x=-\frac{\sqrt{2}}{5}$$