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

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

x uchun yechish

$$x = \frac{10000}{67} = 149\frac{17}{67} \approx 149,253731343$$

$$x=0$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

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

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

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

2 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

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

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

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

2 daraja ko‘rsatkichini 10 ga hisoblang va 100 ni qiymatni oling.

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

2 daraja ko‘rsatkichini \sqrt{300x-2x^{2}} ga hisoblang va 300x-2x^{2} ni qiymatni oling.

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

100 ga 300x-2x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Shartlarni qayta saralash.

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

200x^{2} ni ikki tarafga qo’shing.

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

201x^{2} ni olish uchun x^{2} va 200x^{2} ni birlashtirish.

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

Ikkala tarafdan 30000x ni ayirish.

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

x omili.

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

Tenglamani yechish uchun x=0 va 201x-30000=0 ni yeching.

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

1x=10\sqrt{300x-2x^{2}} tenglamasida x uchun 0 ni almashtiring.

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

Qisqartirish. x=0 tenglamani qoniqtiradi.

$$0=0$$

1x=10\sqrt{300x-2x^{2}} tenglamasida x uchun \frac{10000}{67} ni almashtiring.

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

Qisqartirish. x=\frac{10000}{67} tenglamani qoniqtiradi.

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

x=10\sqrt{300x-2x^{2}} boʻyicha barcha yechimlar roʻyxati.

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