64x^2-9=0 eching

$$64 x ^ { 2 } - 9 = 0$$

x uchun yechish

$$x=\frac{3}{8}=0,375$$

$$x=-\frac{3}{8}=-0,375$$

Kvadratlar farqidan foydalangan qadamlar

Hisoblang: 64x^{2}-9. 64x^{2}-9 ni \left(8x\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).

$$\left(8x-3\right)\left(8x+3\right)=0$$

Tenglamani yechish uchun 8x-3=0 va 8x+3=0 ni yeching.

$$x=\frac{3}{8} x=-\frac{3}{8}$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$64x^{2}=9$$

Ikki tarafini 64 ga bo‘ling.

$$x^{2}=\frac{9}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{3}{8} x=-\frac{3}{8}$$

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.

$$64x^{2}-9=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 64 ni a, 0 ni b va -9 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 64\left(-9\right)}}{2\times 64}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 64\left(-9\right)}}{2\times 64}$$

-4 ni 64 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-256\left(-9\right)}}{2\times 64}$$

-256 ni -9 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{2304}}{2\times 64}$$

2304 ning kvadrat ildizini chiqarish.

$$x=\frac{0±48}{2\times 64}$$

2 ni 64 marotabaga ko'paytirish.

$$x=\frac{0±48}{128}$$

x=\frac{0±48}{128} tenglamasini yeching, bunda ± musbat. \frac{48}{128} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{3}{8}$$

x=\frac{0±48}{128} tenglamasini yeching, bunda ± manfiy. \frac{-48}{128} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{3}{8}$$

Tenglama yechildi.

$$x=\frac{3}{8} x=-\frac{3}{8}$$