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

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

Datrys ar gyfer x

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

$$x=0$$

Camau Ateb

Sgwariwch ddwy ochr yr hafaliad.

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

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

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

Cyfrifo 1 i bŵer 2 a chael 1.

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

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

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

Cyfrifo 10 i bŵer 2 a chael 100.

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

Cyfrifo \sqrt{300x-2x^{2}} i bŵer 2 a chael 300x-2x^{2}.

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

Defnyddio’r briodwedd ddosbarthu i luosi 100 â 300x-2x^{2}.

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

Aildrefnu'r termau.

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

Ychwanegu 200x^{2} at y ddwy ochr.

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

Cyfuno x^{2} a 200x^{2} i gael 201x^{2}.

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

Tynnu 30000x o'r ddwy ochr.

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

Ffactora allan x.

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

I ddod o hyd i atebion hafaliad, datryswch x=0 a 201x-30000=0.

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

Amnewid 0 am x yn yr hafaliad 1x=10\sqrt{300x-2x^{2}}.

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

Symleiddio. Mae'r gwerth x=0 yn bodloni'r hafaliad.

$$0=0$$

Amnewid \frac{10000}{67} am x yn yr hafaliad 1x=10\sqrt{300x-2x^{2}}.

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

Symleiddio. Mae'r gwerth x=\frac{10000}{67} yn bodloni'r hafaliad.

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

Rhestr o'r holl atebion x=10\sqrt{300x-2x^{2}}.

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