(2x+1)^2-4(x+1)^2leq-2 eching

$$( 2 x + 1 ) ^ { 2 } - 4 ( x + 1 ) ^ { 2 } \leq - 2$$

x uchun yechish

$$x\geq -\frac{1}{4}$$

Yechim qadamlari

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

$$4x^{2}+4x+1-4\left(x+1\right)^{2}\leq -2$$

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

$$4x^{2}+4x+1-4\left(x^{2}+2x+1\right)\leq -2$$

-4 ga x^{2}+2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+4x+1-4x^{2}-8x-4\leq -2$$

0 ni olish uchun 4x^{2} va -4x^{2} ni birlashtirish.

$$4x+1-8x-4\leq -2$$

-4x ni olish uchun 4x va -8x ni birlashtirish.

$$-4x+1-4\leq -2$$

-3 olish uchun 1 dan 4 ni ayirish.

$$-4x-3\leq -2$$

3 ni ikki tarafga qo’shing.

$$-4x\leq -2+3$$

1 olish uchun -2 va 3'ni qo'shing.

$$-4x\leq 1$$

Ikki tarafini -4 ga bo‘ling. -4 manfiy boʻlgani uchun tengsizlikning yo‘nalishi o‘zgaradi.

$$x\geq -\frac{1}{4}$$