(8x)^2=1 eching

$$( 8 x ) ^ { 2 } = 1$$

x uchun yechish

$$x=\frac{1}{8}=0,125$$

$$x=-\frac{1}{8}=-0,125$$

Kvadratlar farqidan foydalangan qadamlar

\left(8x\right)^{2} ni kengaytirish.

$$8^{2}x^{2}=1$$

2 daraja ko‘rsatkichini 8 ga hisoblang va 64 ni qiymatni oling.

$$64x^{2}=1$$

Ikkala tarafdan 1 ni ayirish.

$$64x^{2}-1=0$$

Hisoblang: 64x^{2}-1. 64x^{2}-1 ni \left(8x\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).

$$\left(8x-1\right)\left(8x+1\right)=0$$

Tenglamani yechish uchun 8x-1=0 va 8x+1=0 ni yeching.

$$x=\frac{1}{8} x=-\frac{1}{8}$$

Kvadrat ildizini topish bo'yicha qadamlar

\left(8x\right)^{2} ni kengaytirish.

$$8^{2}x^{2}=1$$

2 daraja ko‘rsatkichini 8 ga hisoblang va 64 ni qiymatni oling.

$$64x^{2}=1$$

Ikki tarafini 64 ga bo‘ling.

$$x^{2}=\frac{1}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{1}{8} x=-\frac{1}{8}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(8x\right)^{2} ni kengaytirish.

$$8^{2}x^{2}=1$$

2 daraja ko‘rsatkichini 8 ga hisoblang va 64 ni qiymatni oling.

$$64x^{2}=1$$

Ikkala tarafdan 1 ni ayirish.

$$64x^{2}-1=0$$

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 -1 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 64\left(-1\right)}}{2\times 64}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 64\left(-1\right)}}{2\times 64}$$

-4 ni 64 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-256\left(-1\right)}}{2\times 64}$$

-256 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{256}}{2\times 64}$$

256 ning kvadrat ildizini chiqarish.

$$x=\frac{0±16}{2\times 64}$$

2 ni 64 marotabaga ko'paytirish.

$$x=\frac{0±16}{128}$$

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

$$x=\frac{1}{8}$$

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

$$x=-\frac{1}{8}$$

Tenglama yechildi.

$$x=\frac{1}{8} x=-\frac{1}{8}$$