(x+2/2)^3-(x+1)^2+x^2=x^2(x/8+3/4) eching

$$( \frac { x + 2 } { 2 } ) ^ { 3 } - ( x + 1 ) ^ { 2 } + x ^ { 2 } = x ^ { 2 } ( \frac { x } { 8 } + \frac { 3 } { 4 } )$$

x uchun yechish

$$x=0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 8 ga, 8,4 ning eng kichik karralisiga ko‘paytiring.

$$8\left(\left(\frac{x+2}{2}\right)^{3}-\left(x+1\right)^{2}\right)+8x^{2}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

\frac{x+2}{2}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$8\left(\frac{\left(x+2\right)^{3}}{2^{3}}-\left(x+1\right)^{2}\right)+8x^{2}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

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

$$8\left(\frac{\left(x+2\right)^{3}}{2^{3}}-\left(x^{2}+2x+1\right)\right)+8x^{2}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

x^{2}+2x+1 teskarisini topish uchun har birining teskarisini toping.

$$8\left(\frac{\left(x+2\right)^{3}}{2^{3}}-x^{2}-2x-1\right)+8x^{2}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

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

$$8\left(\frac{\left(x+2\right)^{3}}{2^{3}}+\frac{\left(-x^{2}-2x-1\right)\times 2^{3}}{2^{3}}\right)+8x^{2}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

\frac{\left(x+2\right)^{3}}{2^{3}} va \frac{\left(-x^{2}-2x-1\right)\times 2^{3}}{2^{3}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$8\times \frac{\left(x+2\right)^{3}+\left(-x^{2}-2x-1\right)\times 2^{3}}{2^{3}}+8x^{2}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

\left(x+2\right)^{3}+\left(-x^{2}-2x-1\right)\times 2^{3} ichidagi ko‘paytirishlarni bajaring.

$$8\times \frac{x^{3}+3x^{2}\times 2+3x\times 2^{2}+2^{3}-8x^{2}-16x-8}{2^{3}}+8x^{2}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

x^{3}+3x^{2}\times 2+3x\times 2^{2}+2^{3}-8x^{2}-16x-8 kabi iboralarga o‘xshab birlashtiring.

$$8\times \frac{x^{3}-2x^{2}-4x}{2^{3}}+8x^{2}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

8\times \frac{x^{3}-2x^{2}-4x}{2^{3}} ni yagona kasrga aylantiring.

$$\frac{8\left(x^{3}-2x^{2}-4x\right)}{2^{3}}+8x^{2}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 8x^{2} ni \frac{2^{3}}{2^{3}} marotabaga ko'paytirish.

$$\frac{8\left(x^{3}-2x^{2}-4x\right)}{2^{3}}+\frac{8x^{2}\times 2^{3}}{2^{3}}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

\frac{8\left(x^{3}-2x^{2}-4x\right)}{2^{3}} va \frac{8x^{2}\times 2^{3}}{2^{3}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{8\left(x^{3}-2x^{2}-4x\right)+8x^{2}\times 2^{3}}{2^{3}}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

8\left(x^{3}-2x^{2}-4x\right)+8x^{2}\times 2^{3} ichidagi ko‘paytirishlarni bajaring.

$$\frac{8x^{3}-16x^{2}-32x+64x^{2}}{2^{3}}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

8x^{3}-16x^{2}-32x+64x^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{8x^{3}+48x^{2}-32x}{2^{3}}=8x^{2}\left(\frac{x}{8}+\frac{3}{4}\right)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 8 va 4 ning eng kichik umumiy karralisi 8. \frac{3}{4} ni \frac{2}{2} marotabaga ko'paytirish.

$$\frac{8x^{3}+48x^{2}-32x}{2^{3}}=8x^{2}\left(\frac{x}{8}+\frac{3\times 2}{8}\right)$$

\frac{x}{8} va \frac{3\times 2}{8} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{8x^{3}+48x^{2}-32x}{2^{3}}=8x^{2}\times \frac{x+3\times 2}{8}$$

x+3\times 2 ichidagi ko‘paytirishlarni bajaring.

$$\frac{8x^{3}+48x^{2}-32x}{2^{3}}=8x^{2}\times \frac{x+6}{8}$$

8\times \frac{x+6}{8} ni yagona kasrga aylantiring.

$$\frac{8x^{3}+48x^{2}-32x}{2^{3}}=\frac{8\left(x+6\right)}{8}x^{2}$$

8 va 8 ni qisqartiring.

$$\frac{8x^{3}+48x^{2}-32x}{2^{3}}=\left(x+6\right)x^{2}$$

x+6 ga x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{8x^{3}+48x^{2}-32x}{2^{3}}=x^{3}+6x^{2}$$

3 daraja ko‘rsatkichini 2 ga hisoblang va 8 ni qiymatni oling.

$$\frac{8x^{3}+48x^{2}-32x}{8}=x^{3}+6x^{2}$$

-4x+6x^{2}+x^{3} natijani olish uchun 8x^{3}+48x^{2}-32x ning har bir ifodasini 8 ga bo‘ling.

$$-4x+6x^{2}+x^{3}=x^{3}+6x^{2}$$

Ikkala tarafdan x^{3} ni ayirish.

$$-4x+6x^{2}+x^{3}-x^{3}=6x^{2}$$

0 ni olish uchun x^{3} va -x^{3} ni birlashtirish.

$$-4x+6x^{2}=6x^{2}$$

Ikkala tarafdan 6x^{2} ni ayirish.

$$-4x+6x^{2}-6x^{2}=0$$

0 ni olish uchun 6x^{2} va -6x^{2} ni birlashtirish.

$$-4x=0$$

Ikki son koʻpaytmasi 0 ga teng, agar kamida bittasi 0 bo‘lsa. -4 0 ga teng bo‘lmasa, x 0 ga teng bo‘lishi kerak.

$$x=0$$