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

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

Whakaoti mō x

$$x=4$$

Ngā Upane Otinga

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

$$\sqrt{x-3}=3-\sqrt{x}$$

Pūruatia ngā taha e rua o te whārite.

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

Tātaihia te \sqrt{x-3} mā te pū o 2, kia riro ko x-3.

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

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

$$x-3=9-6\sqrt{x}+\left(\sqrt{x}\right)^{2}$$

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

$$x-3=9-6\sqrt{x}+x$$

Me tāpiri te 6\sqrt{x} ki ngā taha e rua.

$$x-3+6\sqrt{x}=9+x$$

Tangohia te x mai i ngā taha e rua.

$$x-3+6\sqrt{x}-x=9$$

Pahekotia te x me -x, ka 0.

$$-3+6\sqrt{x}=9$$

Me tāpiri te 3 ki ngā taha e rua.

$$6\sqrt{x}=9+3$$

Tāpirihia te 9 ki te 3, ka 12.

$$6\sqrt{x}=12$$

Whakawehea ngā taha e rua ki te 6.

$$\sqrt{x}=\frac{12}{6}$$

Whakawehea te 12 ki te 6, kia riro ko 2.

$$\sqrt{x}=2$$

Pūruatia ngā taha e rua o te whārite.

$$x=4$$

Whakakapia te 4 mō te x i te whārite \sqrt{x-3}+\sqrt{x}=3.

$$\sqrt{4-3}+\sqrt{4}=3$$

Whakarūnātia. Ko te uara x=4 kua ngata te whārite.

$$3=3$$

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

$$x=4$$