Whakaoti i te (2-3x)^2-(3x-1)(3x+1)=2

$$( 2 - 3 x ) ^ { 2 } - ( 3 x - 1 ) ( 3 x + 1 ) = 2$$

Whakaoti mō x

$$x=\frac{1}{4}=0.25$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2-3x\right)^{2}.

$$4-12x+9x^{2}-\left(3x-1\right)\left(3x+1\right)=2$$

Whakaarohia te \left(3x-1\right)\left(3x+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.

$$4-12x+9x^{2}-\left(\left(3x\right)^{2}-1\right)=2$$

Whakarohaina te \left(3x\right)^{2}.

$$4-12x+9x^{2}-\left(3^{2}x^{2}-1\right)=2$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$4-12x+9x^{2}-\left(9x^{2}-1\right)=2$$

Hei kimi i te tauaro o 9x^{2}-1, kimihia te tauaro o ia taurangi.

$$4-12x+9x^{2}-9x^{2}+1=2$$

Pahekotia te 9x^{2} me -9x^{2}, ka 0.

$$4-12x+1=2$$

Tāpirihia te 4 ki te 1, ka 5.

$$5-12x=2$$

Tangohia te 5 mai i ngā taha e rua.

$$-12x=2-5$$

Tangohia te 5 i te 2, ka -3.

$$-12x=-3$$

Whakawehea ngā taha e rua ki te -12.

$$x=\frac{-3}{-12}$$

Whakahekea te hautanga \frac{-3}{-12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -3.

$$x=\frac{1}{4}$$