(2x-1)^2-(3x+4)^2=-5x(x+8) eching

$$( 2 x - 1 ) ^ { 2 } - ( 3 x + 4 ) ^ { 2 } = - 5 x ( x + 8 )$$

x uchun yechish

$$x = \frac{5}{4} = 1\frac{1}{4} = 1,25$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$4x^{2}-4x+1-\left(3x+4\right)^{2}=-5x\left(x+8\right)$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(3x+4\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-4x+1-\left(9x^{2}+24x+16\right)=-5x\left(x+8\right)$$

9x^{2}+24x+16 teskarisini topish uchun har birining teskarisini toping.

$$4x^{2}-4x+1-9x^{2}-24x-16=-5x\left(x+8\right)$$

-5x^{2} ni olish uchun 4x^{2} va -9x^{2} ni birlashtirish.

$$-5x^{2}-4x+1-24x-16=-5x\left(x+8\right)$$

-28x ni olish uchun -4x va -24x ni birlashtirish.

$$-5x^{2}-28x+1-16=-5x\left(x+8\right)$$

-15 olish uchun 1 dan 16 ni ayirish.

$$-5x^{2}-28x-15=-5x\left(x+8\right)$$

-5x ga x+8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-5x^{2}-28x-15=-5x^{2}-40x$$

5x^{2} ni ikki tarafga qo’shing.

$$-5x^{2}-28x-15+5x^{2}=-40x$$

0 ni olish uchun -5x^{2} va 5x^{2} ni birlashtirish.

$$-28x-15=-40x$$

40x ni ikki tarafga qo’shing.

$$-28x-15+40x=0$$

12x ni olish uchun -28x va 40x ni birlashtirish.

$$12x-15=0$$

15 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$12x=15$$

Ikki tarafini 12 ga bo‘ling.

$$x=\frac{15}{12}$$

\frac{15}{12} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{5}{4}$$