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

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

Whakaoti mō x (complex solution)

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

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

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

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

$$x-3=2-x$$

Me tāpiri te x ki ngā taha e rua.

$$x-3+x=2$$

Pahekotia te x me x, ka 2x.

$$2x-3=2$$

Me tāpiri te 3 ki ngā taha e rua.

$$2x=2+3$$

Tāpirihia te 2 ki te 3, ka 5.

$$2x=5$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{5}{2}$$

Whakakapia te \frac{5}{2} mō te x i te whārite \sqrt{x-3}=\sqrt{2-x}.

$$\sqrt{\frac{5}{2}-3}=\sqrt{2-\frac{5}{2}}$$

Whakarūnātia. Ko te uara x=\frac{5}{2} kua ngata te whārite.

$$\frac{1}{2}i\times 2^{\frac{1}{2}}=\frac{1}{2}i\times 2^{\frac{1}{2}}$$

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

$$x=\frac{5}{2}$$