4x^2-9=0 eching

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

x uchun yechish

$$x = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1,5$$

Kvadratlar farqidan foydalangan qadamlar

Hisoblang: 4x^{2}-9. 4x^{2}-9 ni \left(2x\right)^{2}-3^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-3\right)\left(2x+3\right)=0$$

Tenglamani yechish uchun 2x-3=0 va 2x+3=0 ni yeching.

$$x=\frac{3}{2} x=-\frac{3}{2}$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$4x^{2}=9$$

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{3}{2} x=-\frac{3}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

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

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 -9 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-9\right)}}{2\times 4}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 4\left(-9\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-16\left(-9\right)}}{2\times 4}$$

-16 ni -9 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{144}}{2\times 4}$$

144 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±12}{8}$$

x=\frac{0±12}{8} tenglamasini yeching, bunda ± musbat. \frac{12}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{3}{2}$$

x=\frac{0±12}{8} tenglamasini yeching, bunda ± manfiy. \frac{-12}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{3}{2}$$

Tenglama yechildi.

$$x=\frac{3}{2} x=-\frac{3}{2}$$