6x^2-3/8=0 eching

$$6 x ^ { 2 } - \frac { 3 } { 8 } = 0$$

x uchun yechish

$$x=\frac{1}{4}=0,25$$

$$x=-\frac{1}{4}=-0,25$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini \frac{3}{8} ga bo‘ling.

$$16x^{2}-1=0$$

Hisoblang: 16x^{2}-1. 16x^{2}-1 ni \left(4x\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).

$$\left(4x-1\right)\left(4x+1\right)=0$$

Tenglamani yechish uchun 4x-1=0 va 4x+1=0 ni yeching.

$$x=\frac{1}{4} x=-\frac{1}{4}$$

Kvadrat ildizini topish bo'yicha qadamlar

\frac{3}{8} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$6x^{2}=\frac{3}{8}$$

Ikki tarafini 6 ga bo‘ling.

$$x^{2}=\frac{\frac{3}{8}}{6}$$

\frac{\frac{3}{8}}{6} ni yagona kasrga aylantiring.

$$x^{2}=\frac{3}{8\times 6}$$

48 hosil qilish uchun 8 va 6 ni ko'paytirish.

$$x^{2}=\frac{3}{48}$$

\frac{3}{48} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{1}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{1}{4} x=-\frac{1}{4}$$

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.

$$6x^{2}-\frac{3}{8}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, 0 ni b va -\frac{3}{8} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-\frac{3}{8}\right)}}{2\times 6}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 6\left(-\frac{3}{8}\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-24\left(-\frac{3}{8}\right)}}{2\times 6}$$

-24 ni -\frac{3}{8} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{9}}{2\times 6}$$

9 ning kvadrat ildizini chiqarish.

$$x=\frac{0±3}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±3}{12}$$

x=\frac{0±3}{12} tenglamasini yeching, bunda ± musbat. \frac{3}{12} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

x=\frac{0±3}{12} tenglamasini yeching, bunda ± manfiy. \frac{-3}{12} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{4}$$

Tenglama yechildi.

$$x=\frac{1}{4} x=-\frac{1}{4}$$