Whakaoti i te sqrt{2x+4}-2sqrt{x-4}=0

$$\sqrt { 2 x + 4 } - 2 \sqrt { x - 4 } = 0$$

Whakaoti mō x

$$x=10$$

Ngā Upane Otinga

Me tango -2\sqrt{x-4} mai i ngā taha e rua o te whārite.

$$\sqrt{2x+4}=2\sqrt{x-4}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{2x+4}\right)^{2}=\left(2\sqrt{x-4}\right)^{2}$$

Tātaihia te \sqrt{2x+4} mā te pū o 2, kia riro ko 2x+4.

$$2x+4=\left(2\sqrt{x-4}\right)^{2}$$

Whakarohaina te \left(2\sqrt{x-4}\right)^{2}.

$$2x+4=2^{2}\left(\sqrt{x-4}\right)^{2}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$2x+4=4\left(\sqrt{x-4}\right)^{2}$$

Tātaihia te \sqrt{x-4} mā te pū o 2, kia riro ko x-4.

$$2x+4=4\left(x-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x-4.

$$2x+4=4x-16$$

Tangohia te 4x mai i ngā taha e rua.

$$2x+4-4x=-16$$

Pahekotia te 2x me -4x, ka -2x.

$$-2x+4=-16$$

Tangohia te 4 mai i ngā taha e rua.

$$-2x=-16-4$$

Tangohia te 4 i te -16, ka -20.

$$-2x=-20$$

Whakawehea ngā taha e rua ki te -2.

$$x=\frac{-20}{-2}$$

Whakawehea te -20 ki te -2, kia riro ko 10.

$$x=10$$

Whakakapia te 10 mō te x i te whārite \sqrt{2x+4}-2\sqrt{x-4}=0.

$$\sqrt{2\times 10+4}-2\sqrt{10-4}=0$$

Whakarūnātia. Ko te uara x=10 kua ngata te whārite.

$$0=0$$

Ko te whārite \sqrt{2x+4}=2\sqrt{x-4} he rongoā ahurei.

$$x=10$$