Whakaoti i te sqrt{2x+33}-sqrt{2x}=3

$$\sqrt { 2 x + 33 } - \sqrt { 2 x } = 3$$

Whakaoti mō x

$$x=8$$

Ngā Upane Otinga

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

$$\sqrt{2x+33}=3+\sqrt{2x}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{2x+33}\right)^{2}=\left(3+\sqrt{2x}\right)^{2}$$

Tātaihia te \sqrt{2x+33} mā te pū o 2, kia riro ko 2x+33.

$$2x+33=\left(3+\sqrt{2x}\right)^{2}$$

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

$$2x+33=9+6\sqrt{2x}+\left(\sqrt{2x}\right)^{2}$$

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

$$2x+33=9+6\sqrt{2x}+2x$$

Tangohia te 6\sqrt{2x} mai i ngā taha e rua.

$$2x+33-6\sqrt{2x}=9+2x$$

Tangohia te 2x mai i ngā taha e rua.

$$2x+33-6\sqrt{2x}-2x=9$$

Pahekotia te 2x me -2x, ka 0.

$$33-6\sqrt{2x}=9$$

Tangohia te 33 mai i ngā taha e rua.

$$-6\sqrt{2x}=9-33$$

Tangohia te 33 i te 9, ka -24.

$$-6\sqrt{2x}=-24$$

Whakawehea ngā taha e rua ki te -6.

$$\sqrt{2x}=\frac{-24}{-6}$$

Whakawehea te -24 ki te -6, kia riro ko 4.

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

Pūruatia ngā taha e rua o te whārite.

$$2x=16$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x}{2}=\frac{16}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x=\frac{16}{2}$$

Whakawehe 16 ki te 2.

$$x=8$$

Whakakapia te 8 mō te x i te whārite \sqrt{2x+33}-\sqrt{2x}=3.

$$\sqrt{2\times 8+33}-\sqrt{2\times 8}=3$$

Whakarūnātia. Ko te uara x=8 kua ngata te whārite.

$$3=3$$

Ko te whārite \sqrt{2x+33}=\sqrt{2x}+3 he rongoā ahurei.

$$x=8$$