Whakaoti i te sqrt{2x^2-9}-x=0

$$\sqrt { 2 x ^ { 2 } - 9 } - x = 0$$

Whakaoti mō x

$$x=3$$

Ngā Upane Otinga

Me tango -x mai i ngā taha e rua o te whārite.

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

Pūruatia ngā taha e rua o te whārite.

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

Tātaihia te \sqrt{2x^{2}-9} mā te pū o 2, kia riro ko 2x^{2}-9.

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

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

$$2x^{2}-9-x^{2}=0$$

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

$$x^{2}-9=0$$

Whakaarohia te x^{2}-9. Tuhia anō te x^{2}-9 hei x^{2}-3^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-3\right)\left(x+3\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-3=0 me te x+3=0.

$$x=3 x=-3$$

Whakakapia te 3 mō te x i te whārite \sqrt{2x^{2}-9}-x=0.

$$\sqrt{2\times 3^{2}-9}-3=0$$

Whakarūnātia. Ko te uara x=3 kua ngata te whārite.

$$0=0$$

Whakakapia te -3 mō te x i te whārite \sqrt{2x^{2}-9}-x=0.

$$\sqrt{2\left(-3\right)^{2}-9}-\left(-3\right)=0$$

Whakarūnātia. Ko te uara x=-3 kāore e ngata ana ki te whārite.

$$6=0$$

Ko te whārite \sqrt{2x^{2}-9}=x he rongoā ahurei.

$$x=3$$