Whakaoti i te (sqrt{2}x-3)(sqrt{2}x+3)=2x(x-3)

$$( \sqrt { 2 } x - 3 ) ( \sqrt { 2 } x + 3 ) = 2 x ( x - 3 )$$

Whakaoti mō x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakaarohia te \left(\sqrt{2}x-3\right)\left(\sqrt{2}x+3\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 3.

$$\left(\sqrt{2}x\right)^{2}-9=2x\left(x-3\right)$$

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

$$\left(\sqrt{2}\right)^{2}x^{2}-9=2x\left(x-3\right)$$

Ko te pūrua o \sqrt{2} ko 2.

$$2x^{2}-9=2x\left(x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-3.

$$2x^{2}-9=2x^{2}-6x$$

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

$$2x^{2}-9-2x^{2}=-6x$$

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

$$-9=-6x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-6x=-9$$

Whakawehea ngā taha e rua ki te -6.

$$x=\frac{-9}{-6}$$

Whakahekea te hautanga \frac{-9}{-6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -3.

$$x=\frac{3}{2}$$