Whakaoti i te 1(x)=10sqrt{300x-2x^2}

$$1 ( x ) = 10 \sqrt { 300 x - 2 x ^ { 2 } }$$

Whakaoti mō x

$$x = \frac{10000}{67} = 149\frac{17}{67} \approx 149.253731343$$

$$x=0$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(1x\right)^{2}=\left(10\sqrt{300x-2x^{2}}\right)^{2}$$

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

$$1^{2}x^{2}=\left(10\sqrt{300x-2x^{2}}\right)^{2}$$

Tātaihia te 1 mā te pū o 2, kia riro ko 1.

$$1x^{2}=\left(10\sqrt{300x-2x^{2}}\right)^{2}$$

Whakarohaina te \left(10\sqrt{300x-2x^{2}}\right)^{2}.

$$1x^{2}=10^{2}\left(\sqrt{300x-2x^{2}}\right)^{2}$$

Tātaihia te 10 mā te pū o 2, kia riro ko 100.

$$1x^{2}=100\left(\sqrt{300x-2x^{2}}\right)^{2}$$

Tātaihia te \sqrt{300x-2x^{2}} mā te pū o 2, kia riro ko 300x-2x^{2}.

$$1x^{2}=100\left(300x-2x^{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 100 ki te 300x-2x^{2}.

$$1x^{2}=30000x-200x^{2}$$

Whakaraupapatia anō ngā kīanga tau.

$$x^{2}=-200x^{2}+30000x$$

Me tāpiri te 200x^{2} ki ngā taha e rua.

$$x^{2}+200x^{2}=30000x$$

Pahekotia te x^{2} me 200x^{2}, ka 201x^{2}.

$$201x^{2}=30000x$$

Tangohia te 30000x mai i ngā taha e rua.

$$201x^{2}-30000x=0$$

Tauwehea te x.

$$x\left(201x-30000\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 201x-30000=0.

$$x=0 x=\frac{10000}{67}$$

Whakakapia te 0 mō te x i te whārite 1x=10\sqrt{300x-2x^{2}}.

$$1\times 0=10\sqrt{300\times 0-2\times 0^{2}}$$

Whakarūnātia. Ko te uara x=0 kua ngata te whārite.

$$0=0$$

Whakakapia te \frac{10000}{67} mō te x i te whārite 1x=10\sqrt{300x-2x^{2}}.

$$1\times \frac{10000}{67}=10\sqrt{300\times \frac{10000}{67}-2\times \left(\frac{10000}{67}\right)^{2}}$$

Whakarūnātia. Ko te uara x=\frac{10000}{67} kua ngata te whārite.

$$\frac{10000}{67}=\frac{10000}{67}$$

Rārangihia ngā rongoā katoa o x=10\sqrt{300x-2x^{2}}.

$$x=0 x=\frac{10000}{67}$$