sqrt{1-x^2/10}=1-x/3 eching

$$\sqrt { 1 - \frac { x ^ { 2 } } { 10 } } = 1 - \frac { x } { 3 }$$

x uchun yechish

$$x=0$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{1-\frac{x^{2}}{10}}\right)^{2}=\left(1-\frac{x}{3}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{1-\frac{x^{2}}{10}} ga hisoblang va 1-\frac{x^{2}}{10} ni qiymatni oling.

$$1-\frac{x^{2}}{10}=\left(1-\frac{x}{3}\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(1-\frac{x}{3}\right)^{2} kengaytirilishi uchun ishlating.

$$1-\frac{x^{2}}{10}=1+2\left(-\frac{x}{3}\right)+\left(-\frac{x}{3}\right)^{2}$$

2\left(-\frac{x}{3}\right) ni yagona kasrga aylantiring.

$$1-\frac{x^{2}}{10}=1+\frac{-2x}{3}+\left(-\frac{x}{3}\right)^{2}$$

2 daraja ko‘rsatkichini -\frac{x}{3} ga hisoblang va \left(\frac{x}{3}\right)^{2} ni qiymatni oling.

$$1-\frac{x^{2}}{10}=1+\frac{-2x}{3}+\left(\frac{x}{3}\right)^{2}$$

\frac{x}{3}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$1-\frac{x^{2}}{10}=1+\frac{-2x}{3}+\frac{x^{2}}{3^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{3^{2}}{3^{2}} marotabaga ko'paytirish.

$$1-\frac{x^{2}}{10}=\frac{3^{2}}{3^{2}}+\frac{-2x}{3}+\frac{x^{2}}{3^{2}}$$

\frac{3^{2}}{3^{2}} va \frac{x^{2}}{3^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$1-\frac{x^{2}}{10}=\frac{3^{2}+x^{2}}{3^{2}}+\frac{-2x}{3}$$

3^{2}+x^{2} kabi iboralarga o‘xshab birlashtiring.

$$1-\frac{x^{2}}{10}=\frac{9+x^{2}}{3^{2}}+\frac{-2x}{3}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3^{2} va 3 ning eng kichik umumiy karralisi 9. \frac{-2x}{3} ni \frac{3}{3} marotabaga ko'paytirish.

$$1-\frac{x^{2}}{10}=\frac{9+x^{2}}{9}+\frac{3\left(-2\right)x}{9}$$

\frac{9+x^{2}}{9} va \frac{3\left(-2\right)x}{9} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$1-\frac{x^{2}}{10}=\frac{9+x^{2}+3\left(-2\right)x}{9}$$

9+x^{2}+3\left(-2\right)x ichidagi ko‘paytirishlarni bajaring.

$$1-\frac{x^{2}}{10}=\frac{9+x^{2}-6x}{9}$$

1+\frac{1}{9}x^{2}-\frac{2}{3}x natijani olish uchun 9+x^{2}-6x ning har bir ifodasini 9 ga bo‘ling.

$$1-\frac{x^{2}}{10}=1+\frac{1}{9}x^{2}-\frac{2}{3}x$$

Tenglamaning ikkala tarafini 90 ga, 10,9,3 ning eng kichik karralisiga ko‘paytiring.

$$90-9x^{2}=90+10x^{2}-60x$$

Ikkala tarafdan 90 ni ayirish.

$$90-9x^{2}-90=10x^{2}-60x$$

0 olish uchun 90 dan 90 ni ayirish.

$$-9x^{2}=10x^{2}-60x$$

Ikkala tarafdan 10x^{2} ni ayirish.

$$-9x^{2}-10x^{2}=-60x$$

-19x^{2} ni olish uchun -9x^{2} va -10x^{2} ni birlashtirish.

$$-19x^{2}=-60x$$

60x ni ikki tarafga qo’shing.

$$-19x^{2}+60x=0$$

x omili.

$$x\left(-19x+60\right)=0$$

Tenglamani yechish uchun x=0 va -19x+60=0 ni yeching.

$$x=0 x=\frac{60}{19}$$

\sqrt{1-\frac{x^{2}}{10}}=1-\frac{x}{3} tenglamasida x uchun 0 ni almashtiring.

$$\sqrt{1-\frac{0^{2}}{10}}=1-\frac{0}{3}$$

Qisqartirish. x=0 tenglamani qoniqtiradi.

$$1=1$$

\sqrt{1-\frac{x^{2}}{10}}=1-\frac{x}{3} tenglamasida x uchun \frac{60}{19} ni almashtiring.

$$\sqrt{1-\frac{\left(\frac{60}{19}\right)^{2}}{10}}=1-\frac{\frac{60}{19}}{3}$$

Qisqartirish. x=\frac{60}{19} qiymati bu tenglamani qoniqtirmaydi, chunki oʻng va chap tarafdagi belgilar bir-biriga qarama-qarshi.

$$\frac{1}{19}=-\frac{1}{19}$$

\sqrt{-\frac{x^{2}}{10}+1}=-\frac{x}{3}+1 tenglamasi noyob yechimga ega.

$$x=0$$