Whakaoti i te 9x+2=sqrt{81x+5}

$$9x+2= \sqrt{ 81x+5 }$$

Whakaoti mō x

$$x=\frac{\sqrt{29}+5}{18}\approx 0.5769536$$

$$x=\frac{5-\sqrt{29}}{18}\approx -0.021398045$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(9x+2\right)^{2}=\left(\sqrt{81x+5}\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(9x+2\right)^{2}.

$$81x^{2}+36x+4=\left(\sqrt{81x+5}\right)^{2}$$

Tātaihia te \sqrt{81x+5} mā te pū o 2, kia riro ko 81x+5.

$$81x^{2}+36x+4=81x+5$$

Tangohia te 81x mai i ngā taha e rua.

$$81x^{2}+36x+4-81x=5$$

Pahekotia te 36x me -81x, ka -45x.

$$81x^{2}-45x+4=5$$

Tangohia te 5 mai i ngā taha e rua.

$$81x^{2}-45x+4-5=0$$

Tangohia te 5 i te 4, ka -1.

$$81x^{2}-45x-1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 81 mō a, -45 mō b, me -1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-45\right)±\sqrt{\left(-45\right)^{2}-4\times 81\left(-1\right)}}{2\times 81}$$

Pūrua -45.

$$x=\frac{-\left(-45\right)±\sqrt{2025-4\times 81\left(-1\right)}}{2\times 81}$$

Whakareatia -4 ki te 81.

$$x=\frac{-\left(-45\right)±\sqrt{2025-324\left(-1\right)}}{2\times 81}$$

Whakareatia -324 ki te -1.

$$x=\frac{-\left(-45\right)±\sqrt{2025+324}}{2\times 81}$$

Tāpiri 2025 ki te 324.

$$x=\frac{-\left(-45\right)±\sqrt{2349}}{2\times 81}$$

Tuhia te pūtakerua o te 2349.

$$x=\frac{-\left(-45\right)±9\sqrt{29}}{2\times 81}$$

Ko te tauaro o -45 ko 45.

$$x=\frac{45±9\sqrt{29}}{2\times 81}$$

Whakareatia 2 ki te 81.

$$x=\frac{45±9\sqrt{29}}{162}$$

Nā, me whakaoti te whārite x=\frac{45±9\sqrt{29}}{162} ina he tāpiri te ±. Tāpiri 45 ki te 9\sqrt{29}.

$$x=\frac{9\sqrt{29}+45}{162}$$

Whakawehe 45+9\sqrt{29} ki te 162.

$$x=\frac{\sqrt{29}+5}{18}$$

Nā, me whakaoti te whārite x=\frac{45±9\sqrt{29}}{162} ina he tango te ±. Tango 9\sqrt{29} mai i 45.

$$x=\frac{45-9\sqrt{29}}{162}$$

Whakawehe 45-9\sqrt{29} ki te 162.

$$x=\frac{5-\sqrt{29}}{18}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{29}+5}{18} x=\frac{5-\sqrt{29}}{18}$$

Whakakapia te \frac{\sqrt{29}+5}{18} mō te x i te whārite 9x+2=\sqrt{81x+5}.

$$9\times \frac{\sqrt{29}+5}{18}+2=\sqrt{81\times \frac{\sqrt{29}+5}{18}+5}$$

Whakarūnātia. Ko te uara x=\frac{\sqrt{29}+5}{18} kua ngata te whārite.

$$\frac{1}{2}\times 29^{\frac{1}{2}}+\frac{9}{2}=\frac{9}{2}+\frac{1}{2}\times 29^{\frac{1}{2}}$$

Whakakapia te \frac{5-\sqrt{29}}{18} mō te x i te whārite 9x+2=\sqrt{81x+5}.

$$9\times \frac{5-\sqrt{29}}{18}+2=\sqrt{81\times \frac{5-\sqrt{29}}{18}+5}$$

Whakarūnātia. Ko te uara x=\frac{5-\sqrt{29}}{18} kua ngata te whārite.

$$\frac{9}{2}-\frac{1}{2}\times 29^{\frac{1}{2}}=\frac{9}{2}-\frac{1}{2}\times 29^{\frac{1}{2}}$$

Rārangihia ngā rongoā katoa o 9x+2=\sqrt{81x+5}.

$$x=\frac{\sqrt{29}+5}{18} x=\frac{5-\sqrt{29}}{18}$$