(x-1)(x^2+x+1)-9-2xleq(x-1)^3+x(3x-2) eching

$$( x - 1 ) ( x ^ { 2 } + x + 1 ) - 9 - 2 x \leq ( x - 1 ) ^ { 3 } + x ( 3 x - 2 )$$

x uchun yechish

$$x\geq -3$$

Yechim qadamlari

x-1 ga x^{2}+x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

-10 olish uchun -1 dan 9 ni ayirish.

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

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

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

x ga 3x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

0 ni olish uchun -3x^{2} va 3x^{2} ni birlashtirish.

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

x ni olish uchun 3x va -2x ni birlashtirish.

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

Ikkala tarafdan x^{3} ni ayirish.

$$x^{3}-10-2x-x^{3}\leq x-1$$

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

$$-10-2x\leq x-1$$

Ikkala tarafdan x ni ayirish.

$$-10-2x-x\leq -1$$

-3x ni olish uchun -2x va -x ni birlashtirish.

$$-10-3x\leq -1$$

10 ni ikki tarafga qo’shing.

$$-3x\leq -1+10$$

9 olish uchun -1 va 10'ni qo'shing.

$$-3x\leq 9$$

Ikki tarafini -3 ga bo‘ling. -3 manfiy boʻlgani uchun tengsizlikning yo‘nalishi o‘zgaradi.

$$x\geq \frac{9}{-3}$$

-3 ni olish uchun 9 ni -3 ga bo‘ling.

$$x\geq -3$$