Whakaoti i te 9(x+1)=sqrt{2x+5}

$$9 ( x + 1 ) = \sqrt { 2 x + 5 }$$

Whakaoti mō x

$$x=\frac{2\left(\sqrt{61}-40\right)}{81}\approx -0.79480865$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(9\left(x+1\right)\right)^{2}=\left(\sqrt{2x+5}\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te x+1.

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

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

$$81x^{2}+162x+81=\left(\sqrt{2x+5}\right)^{2}$$

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

$$81x^{2}+162x+81=2x+5$$

Tangohia te 2x mai i ngā taha e rua.

$$81x^{2}+162x+81-2x=5$$

Pahekotia te 162x me -2x, ka 160x.

$$81x^{2}+160x+81=5$$

Tangohia te 5 mai i ngā taha e rua.

$$81x^{2}+160x+81-5=0$$

Tangohia te 5 i te 81, ka 76.

$$81x^{2}+160x+76=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 81 mō a, 160 mō b, me 76 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-160±\sqrt{160^{2}-4\times 81\times 76}}{2\times 81}$$

Pūrua 160.

$$x=\frac{-160±\sqrt{25600-4\times 81\times 76}}{2\times 81}$$

Whakareatia -4 ki te 81.

$$x=\frac{-160±\sqrt{25600-324\times 76}}{2\times 81}$$

Whakareatia -324 ki te 76.

$$x=\frac{-160±\sqrt{25600-24624}}{2\times 81}$$

Tāpiri 25600 ki te -24624.

$$x=\frac{-160±\sqrt{976}}{2\times 81}$$

Tuhia te pūtakerua o te 976.

$$x=\frac{-160±4\sqrt{61}}{2\times 81}$$

Whakareatia 2 ki te 81.

$$x=\frac{-160±4\sqrt{61}}{162}$$

Nā, me whakaoti te whārite x=\frac{-160±4\sqrt{61}}{162} ina he tāpiri te ±. Tāpiri -160 ki te 4\sqrt{61}.

$$x=\frac{4\sqrt{61}-160}{162}$$

Whakawehe -160+4\sqrt{61} ki te 162.

$$x=\frac{2\sqrt{61}-80}{81}$$

Nā, me whakaoti te whārite x=\frac{-160±4\sqrt{61}}{162} ina he tango te ±. Tango 4\sqrt{61} mai i -160.

$$x=\frac{-4\sqrt{61}-160}{162}$$

Whakawehe -160-4\sqrt{61} ki te 162.

$$x=\frac{-2\sqrt{61}-80}{81}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{61}-80}{81} x=\frac{-2\sqrt{61}-80}{81}$$

Whakakapia te \frac{2\sqrt{61}-80}{81} mō te x i te whārite 9\left(x+1\right)=\sqrt{2x+5}.

$$9\left(\frac{2\sqrt{61}-80}{81}+1\right)=\sqrt{2\times \frac{2\sqrt{61}-80}{81}+5}$$

Whakarūnātia. Ko te uara x=\frac{2\sqrt{61}-80}{81} kua ngata te whārite.

$$\frac{2}{9}\times 61^{\frac{1}{2}}+\frac{1}{9}=\frac{2}{9}\times 61^{\frac{1}{2}}+\frac{1}{9}$$

Whakakapia te \frac{-2\sqrt{61}-80}{81} mō te x i te whārite 9\left(x+1\right)=\sqrt{2x+5}.

$$9\left(\frac{-2\sqrt{61}-80}{81}+1\right)=\sqrt{2\times \frac{-2\sqrt{61}-80}{81}+5}$$

Whakarūnātia. Ko te uara x=\frac{-2\sqrt{61}-80}{81} kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-\frac{2}{9}\times 61^{\frac{1}{2}}+\frac{1}{9}=\frac{2}{9}\times 61^{\frac{1}{2}}-\frac{1}{9}$$

Ko te whārite 9\left(x+1\right)=\sqrt{2x+5} he rongoā ahurei.

$$x=\frac{2\sqrt{61}-80}{81}$$