(x+2)^2-(x+3)^2<3 eching

$$( x + 2 ) ^ { 2 } - ( x + 3 ) ^ { 2 } < 3$$

x uchun yechish

$$x>-4$$

Yechim qadamlari

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

$$x^{2}+4x+4-\left(x+3\right)^{2}<3$$

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

$$x^{2}+4x+4-\left(x^{2}+6x+9\right)<3$$

x^{2}+6x+9 teskarisini topish uchun har birining teskarisini toping.

$$x^{2}+4x+4-x^{2}-6x-9<3$$

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

$$4x+4-6x-9<3$$

-2x ni olish uchun 4x va -6x ni birlashtirish.

$$-2x+4-9<3$$

-5 olish uchun 4 dan 9 ni ayirish.

$$-2x-5<3$$

5 ni ikki tarafga qo’shing.

$$-2x<3+5$$

8 olish uchun 3 va 5'ni qo'shing.

$$-2x<8$$

Ikki tarafini -2 ga bo‘ling. -2 manfiy boʻlgani uchun tengsizlikning yo‘nalishi o‘zgaradi.

$$x>\frac{8}{-2}$$

-4 ni olish uchun 8 ni -2 ga bo‘ling.

$$x>-4$$