Whakaoti i te 18x=0x+36sqrt{1-x^2}

$$18 x = 0 x + 36 \sqrt { 1 - x ^ { 2 } }$$

Whakaoti mō x

$$x=\frac{2\sqrt{5}}{5}\approx 0.894427191$$

Ngā Upane Otinga

Me tango 0 mai i ngā taha e rua o te whārite.

$$18x=36\sqrt{1-x^{2}}$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$18x+0=36\sqrt{1-x^{2}}$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$18x=36\sqrt{1-x^{2}}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(18x\right)^{2}=\left(36\sqrt{1-x^{2}}\right)^{2}$$

Whakarohaina te \left(18x\right)^{2}.

$$18^{2}x^{2}=\left(36\sqrt{1-x^{2}}\right)^{2}$$

Tātaihia te 18 mā te pū o 2, kia riro ko 324.

$$324x^{2}=\left(36\sqrt{1-x^{2}}\right)^{2}$$

Whakarohaina te \left(36\sqrt{1-x^{2}}\right)^{2}.

$$324x^{2}=36^{2}\left(\sqrt{1-x^{2}}\right)^{2}$$

Tātaihia te 36 mā te pū o 2, kia riro ko 1296.

$$324x^{2}=1296\left(\sqrt{1-x^{2}}\right)^{2}$$

Tātaihia te \sqrt{1-x^{2}} mā te pū o 2, kia riro ko 1-x^{2}.

$$324x^{2}=1296\left(1-x^{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1296 ki te 1-x^{2}.

$$324x^{2}=1296-1296x^{2}$$

Me tāpiri te 1296x^{2} ki ngā taha e rua.

$$324x^{2}+1296x^{2}=1296$$

Pahekotia te 324x^{2} me 1296x^{2}, ka 1620x^{2}.

$$1620x^{2}=1296$$

Whakawehea ngā taha e rua ki te 1620.

$$x^{2}=\frac{1296}{1620}$$

Whakahekea te hautanga \frac{1296}{1620} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 324.

$$x^{2}=\frac{4}{5}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

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

Whakakapia te \frac{2\sqrt{5}}{5} mō te x i te whārite 18x=0x+36\sqrt{1-x^{2}}.

$$18\times \frac{2\sqrt{5}}{5}=0\times \frac{2\sqrt{5}}{5}+36\sqrt{1-\left(\frac{2\sqrt{5}}{5}\right)^{2}}$$

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

$$\frac{36}{5}\times 5^{\frac{1}{2}}=\frac{36}{5}\times 5^{\frac{1}{2}}$$

Whakakapia te -\frac{2\sqrt{5}}{5} mō te x i te whārite 18x=0x+36\sqrt{1-x^{2}}.

$$18\left(-\frac{2\sqrt{5}}{5}\right)=0\left(-\frac{2\sqrt{5}}{5}\right)+36\sqrt{1-\left(-\frac{2\sqrt{5}}{5}\right)^{2}}$$

Whakarūnātia. Ko te uara x=-\frac{2\sqrt{5}}{5} kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-\frac{36}{5}\times 5^{\frac{1}{2}}=\frac{36}{5}\times 5^{\frac{1}{2}}$$

Ko te whārite 18x=36\sqrt{1-x^{2}} he rongoā ahurei.

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