Whakaoti i te sqrt{x+5}=x

$$\sqrt{ x+5 } =x$$

Whakaoti mō x

$$x = \frac{\sqrt{21} + 1}{2} \approx 2.791287847$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

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

$$x+5=x^{2}$$

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

$$x+5-x^{2}=0$$

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.

$$-x^{2}+x+5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 1 mō b, me 5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-1±\sqrt{1+4\times 5}}{2\left(-1\right)}$$

Whakareatia 4 ki te 5.

$$x=\frac{-1±\sqrt{1+20}}{2\left(-1\right)}$$

Tāpiri 1 ki te 20.

$$x=\frac{-1±\sqrt{21}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-1±\sqrt{21}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{21}}{-2} ina he tāpiri te ±. Tāpiri -1 ki te \sqrt{21}.

$$x=\frac{\sqrt{21}-1}{-2}$$

Whakawehe -1+\sqrt{21} ki te -2.

$$x=\frac{1-\sqrt{21}}{2}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{21}}{-2} ina he tango te ±. Tango \sqrt{21} mai i -1.

$$x=\frac{-\sqrt{21}-1}{-2}$$

Whakawehe -1-\sqrt{21} ki te -2.

$$x=\frac{\sqrt{21}+1}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{1-\sqrt{21}}{2} x=\frac{\sqrt{21}+1}{2}$$

Whakakapia te \frac{1-\sqrt{21}}{2} mō te x i te whārite \sqrt{x+5}=x.

$$\sqrt{\frac{1-\sqrt{21}}{2}+5}=\frac{1-\sqrt{21}}{2}$$

Whakarūnātia. Ko te uara x=\frac{1-\sqrt{21}}{2} kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-\left(\frac{1}{2}-\frac{1}{2}\times 21^{\frac{1}{2}}\right)=\frac{1}{2}-\frac{1}{2}\times 21^{\frac{1}{2}}$$

Whakakapia te \frac{\sqrt{21}+1}{2} mō te x i te whārite \sqrt{x+5}=x.

$$\sqrt{\frac{\sqrt{21}+1}{2}+5}=\frac{\sqrt{21}+1}{2}$$

Whakarūnātia. Ko te uara x=\frac{\sqrt{21}+1}{2} kua ngata te whārite.

$$\frac{1}{2}+\frac{1}{2}\times 21^{\frac{1}{2}}=\frac{1}{2}\times 21^{\frac{1}{2}}+\frac{1}{2}$$

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

$$x=\frac{\sqrt{21}+1}{2}$$