Whakaoti i te sqrt{x}+x=7-6

$$\sqrt{ x } +x=7-6$$

Whakaoti mō x

$$x=\frac{3-\sqrt{5}}{2}\approx 0.381966011$$

Ngā Upane Otinga

Me tango x mai i ngā taha e rua o te whārite.

$$\sqrt{x}=7-6-x$$

Tangohia te 6 i te 7, ka 1.

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

Pūruatia ngā taha e rua o te whārite.

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

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

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

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

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

Tangohia te 1 mai i ngā taha e rua.

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

Me tāpiri te 2x ki ngā taha e rua.

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

Pahekotia te x me 2x, ka 3x.

$$3x-1=x^{2}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$3x-1-x^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-x^{2}+3x-1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 3 mō b, me -1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\left(-1\right)\left(-1\right)}}{2\left(-1\right)}$$

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\left(-1\right)\left(-1\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-3±\sqrt{9+4\left(-1\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -1.

$$x=\frac{-3±\sqrt{9-4}}{2\left(-1\right)}$$

Tāpiri 9 ki te -4.

$$x=\frac{-3±\sqrt{5}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-3±\sqrt{5}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{5}}{-2} ina he tāpiri te ±. Tāpiri -3 ki te \sqrt{5}.

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

Whakawehe -3+\sqrt{5} ki te -2.

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

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{5}}{-2} ina he tango te ±. Tango \sqrt{5} mai i -3.

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

Whakawehe -3-\sqrt{5} ki te -2.

$$x=\frac{\sqrt{5}+3}{2}$$

Kua oti te whārite te whakatau.

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

Whakakapia te \frac{3-\sqrt{5}}{2} mō te x i te whārite \sqrt{x}+x=7-6.

$$\sqrt{\frac{3-\sqrt{5}}{2}}+\frac{3-\sqrt{5}}{2}=7-6$$

Whakarūnātia. Ko te uara x=\frac{3-\sqrt{5}}{2} kua ngata te whārite.

$$1=1$$

Whakakapia te \frac{\sqrt{5}+3}{2} mō te x i te whārite \sqrt{x}+x=7-6.

$$\sqrt{\frac{\sqrt{5}+3}{2}}+\frac{\sqrt{5}+3}{2}=7-6$$

Whakarūnātia. Ko te uara x=\frac{\sqrt{5}+3}{2} kāore e ngata ana ki te whārite.

$$2+5^{\frac{1}{2}}=1$$

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

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