L=(2x-3)^2-5(2x-3)(x+1) eching

$$L = ( 2 x - 3 ) ^ { 2 } - 5 ( 2 x - 3 ) ( x + 1 )$$

L uchun yechish

$$L=24-7x-6x^{2}$$

Yechim qadamlari

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

$$L=4x^{2}-12x+9-5\left(2x-3\right)\left(x+1\right)$$

-5 ga 2x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$L=4x^{2}-12x+9+\left(-10x+15\right)\left(x+1\right)$$

-10x+15 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$L=4x^{2}-12x+9-10x^{2}+5x+15$$

-6x^{2} ni olish uchun 4x^{2} va -10x^{2} ni birlashtirish.

$$L=-6x^{2}-12x+9+5x+15$$

-7x ni olish uchun -12x va 5x ni birlashtirish.

$$L=-6x^{2}-7x+9+15$$

24 olish uchun 9 va 15'ni qo'shing.

$$L=-6x^{2}-7x+24$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{625-24L}-7}{12}$$

$$x=\frac{-\sqrt{625-24L}-7}{12}$$

x uchun yechish

$$x=\frac{\sqrt{625-24L}-7}{12}$$

$$x=\frac{-\sqrt{625-24L}-7}{12}\text{, }L\leq \frac{625}{24}$$