Whakaoti i te x-1=sqrt{2x}

$$x-1= \sqrt{ 2x }$$

Whakaoti mō x

$$x=\sqrt{3}+2\approx 3.732050808$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(x-1\right)^{2}=\left(\sqrt{2x}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-1\right)^{2}.

$$x^{2}-2x+1=\left(\sqrt{2x}\right)^{2}$$

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

$$x^{2}-2x+1=2x$$

Tangohia te 2x mai i ngā taha e rua.

$$x^{2}-2x+1-2x=0$$

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

$$x^{2}-4x+1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -4 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4}}{2}$$

Tāpiri 16 ki te -4.

$$x=\frac{-\left(-4\right)±\sqrt{12}}{2}$$

Tuhia te pūtakerua o te 12.

$$x=\frac{-\left(-4\right)±2\sqrt{3}}{2}$$

Ko te tauaro o -4 ko 4.

$$x=\frac{4±2\sqrt{3}}{2}$$

Nā, me whakaoti te whārite x=\frac{4±2\sqrt{3}}{2} ina he tāpiri te ±. Tāpiri 4 ki te 2\sqrt{3}.

$$x=\frac{2\sqrt{3}+4}{2}$$

Whakawehe 4+2\sqrt{3} ki te 2.

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

Nā, me whakaoti te whārite x=\frac{4±2\sqrt{3}}{2} ina he tango te ±. Tango 2\sqrt{3} mai i 4.

$$x=\frac{4-2\sqrt{3}}{2}$$

Whakawehe 4-2\sqrt{3} ki te 2.

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

Kua oti te whārite te whakatau.

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

Whakakapia te \sqrt{3}+2 mō te x i te whārite x-1=\sqrt{2x}.

$$\sqrt{3}+2-1=\sqrt{2\left(\sqrt{3}+2\right)}$$

Whakarūnātia. Ko te uara x=\sqrt{3}+2 kua ngata te whārite.

$$3^{\frac{1}{2}}+1=3^{\frac{1}{2}}+1$$

Whakakapia te 2-\sqrt{3} mō te x i te whārite x-1=\sqrt{2x}.

$$2-\sqrt{3}-1=\sqrt{2\left(2-\sqrt{3}\right)}$$

Whakarūnātia. Ko te uara x=2-\sqrt{3} kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$1-3^{\frac{1}{2}}=3^{\frac{1}{2}}-1$$

Ko te whārite x-1=\sqrt{2x} he rongoā ahurei.

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