4(x-3)^2-(2x-5)^2geq2 eching

$$4 ( x - 3 ) ^ { 2 } - ( 2 x - 5 ) ^ { 2 } \geq 2$$

x uchun yechish

$$x\leq \frac{9}{4}$$

Yechim qadamlari

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

$$4\left(x^{2}-6x+9\right)-\left(2x-5\right)^{2}\geq 2$$

4 ga x^{2}-6x+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}-24x+36-\left(2x-5\right)^{2}\geq 2$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2x-5\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-24x+36-\left(4x^{2}-20x+25\right)\geq 2$$

4x^{2}-20x+25 teskarisini topish uchun har birining teskarisini toping.

$$4x^{2}-24x+36-4x^{2}+20x-25\geq 2$$

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

$$-24x+36+20x-25\geq 2$$

-4x ni olish uchun -24x va 20x ni birlashtirish.

$$-4x+36-25\geq 2$$

11 olish uchun 36 dan 25 ni ayirish.

$$-4x+11\geq 2$$

Ikkala tarafdan 11 ni ayirish.

$$-4x\geq 2-11$$

-9 olish uchun 2 dan 11 ni ayirish.

$$-4x\geq -9$$

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

$$x\leq \frac{-9}{-4}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-9}{-4} kasrini \frac{9}{4} ga soddalashtirish mumkin.

$$x\leq \frac{9}{4}$$