x-3/2+4/2x+3=0 eching

$$x - \frac { 3 } { 2 } + \frac { 4 } { 2 x + 3 } = 0$$

x uchun yechish

$$x=-\frac{1}{2}=-0,5$$

$$x=\frac{1}{2}=0,5$$

Kvadratlar farqidan foydalangan qadamlar

x qiymati -\frac{3}{2} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2\left(2x+3\right) ga, 2,2x+3 ning eng kichik karralisiga ko‘paytiring.

$$2\left(2x+3\right)x+2\left(2x+3\right)\left(-\frac{3}{2}\right)+2\times 4=0$$

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

$$\left(4x+6\right)x+2\left(2x+3\right)\left(-\frac{3}{2}\right)+2\times 4=0$$

4x+6 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+6x+2\left(2x+3\right)\left(-\frac{3}{2}\right)+2\times 4=0$$

-3 hosil qilish uchun 2 va -\frac{3}{2} ni ko'paytirish.

$$4x^{2}+6x-3\left(2x+3\right)+2\times 4=0$$

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

$$4x^{2}+6x-6x-9+2\times 4=0$$

0 ni olish uchun 6x va -6x ni birlashtirish.

$$4x^{2}-9+2\times 4=0$$

8 hosil qilish uchun 2 va 4 ni ko'paytirish.

$$4x^{2}-9+8=0$$

-1 olish uchun -9 va 8'ni qo'shing.

$$4x^{2}-1=0$$

Hisoblang: 4x^{2}-1. 4x^{2}-1 ni \left(2x\right)^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-1\right)\left(2x+1\right)=0$$

Tenglamani yechish uchun 2x-1=0 va 2x+1=0 ni yeching.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Kvadrat ildizini topish bo'yicha qadamlar

x qiymati -\frac{3}{2} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2\left(2x+3\right) ga, 2,2x+3 ning eng kichik karralisiga ko‘paytiring.

$$2\left(2x+3\right)x+2\left(2x+3\right)\left(-\frac{3}{2}\right)+2\times 4=0$$

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

$$\left(4x+6\right)x+2\left(2x+3\right)\left(-\frac{3}{2}\right)+2\times 4=0$$

4x+6 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+6x+2\left(2x+3\right)\left(-\frac{3}{2}\right)+2\times 4=0$$

-3 hosil qilish uchun 2 va -\frac{3}{2} ni ko'paytirish.

$$4x^{2}+6x-3\left(2x+3\right)+2\times 4=0$$

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

$$4x^{2}+6x-6x-9+2\times 4=0$$

0 ni olish uchun 6x va -6x ni birlashtirish.

$$4x^{2}-9+2\times 4=0$$

8 hosil qilish uchun 2 va 4 ni ko'paytirish.

$$4x^{2}-9+8=0$$

-1 olish uchun -9 va 8'ni qo'shing.

$$4x^{2}-1=0$$

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

$$4x^{2}=1$$

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{1}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -\frac{3}{2} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2\left(2x+3\right) ga, 2,2x+3 ning eng kichik karralisiga ko‘paytiring.

$$2\left(2x+3\right)x+2\left(2x+3\right)\left(-\frac{3}{2}\right)+2\times 4=0$$

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

$$\left(4x+6\right)x+2\left(2x+3\right)\left(-\frac{3}{2}\right)+2\times 4=0$$

4x+6 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+6x+2\left(2x+3\right)\left(-\frac{3}{2}\right)+2\times 4=0$$

-3 hosil qilish uchun 2 va -\frac{3}{2} ni ko'paytirish.

$$4x^{2}+6x-3\left(2x+3\right)+2\times 4=0$$

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

$$4x^{2}+6x-6x-9+2\times 4=0$$

0 ni olish uchun 6x va -6x ni birlashtirish.

$$4x^{2}-9+2\times 4=0$$

8 hosil qilish uchun 2 va 4 ni ko'paytirish.

$$4x^{2}-9+8=0$$

-1 olish uchun -9 va 8'ni qo'shing.

$$4x^{2}-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 0 ni b va -1 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-1\right)}}{2\times 4}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 4\left(-1\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-16\left(-1\right)}}{2\times 4}$$

-16 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{16}}{2\times 4}$$

16 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±4}{8}$$

x=\frac{0±4}{8} tenglamasini yeching, bunda ± musbat. \frac{4}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{2}$$

x=\frac{0±4}{8} tenglamasini yeching, bunda ± manfiy. \frac{-4}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{2}$$

Tenglama yechildi.

$$x=\frac{1}{2} x=-\frac{1}{2}$$