Whakaoti i te sqrt{x-5}=2sqrt{x}

$$\sqrt{ x-5 } =2 \sqrt{ x }$$

Whakaoti mō x (complex solution)

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x-5}\right)^{2}=\left(2\sqrt{x}\right)^{2}$$

Tātaihia te \sqrt{x-5} mā te pū o 2, kia riro ko x-5.

$$x-5=\left(2\sqrt{x}\right)^{2}$$

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

$$x-5=2^{2}\left(\sqrt{x}\right)^{2}$$

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

$$x-5=4\left(\sqrt{x}\right)^{2}$$

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

$$x-5=4x$$

Tangohia te 4x mai i ngā taha e rua.

$$x-5-4x=0$$

Pahekotia te x me -4x, ka -3x.

$$-3x-5=0$$

Me tāpiri te 5 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$-3x=5$$

Whakawehea ngā taha e rua ki te -3.

$$x=\frac{5}{-3}$$

Ka taea te hautanga \frac{5}{-3} te tuhi anō ko -\frac{5}{3} mā te tango i te tohu tōraro.

$$x=-\frac{5}{3}$$

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

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

Whakarūnātia. Ko te uara x=-\frac{5}{3} kua ngata te whārite.

$$\frac{2}{3}i\times 15^{\frac{1}{2}}=\frac{2}{3}i\times 15^{\frac{1}{2}}$$

Ko te whārite \sqrt{x-5}=2\sqrt{x} he rongoā ahurei.

$$x=-\frac{5}{3}$$