25x^2=4? eching

$$25 x ^ { 2 } = 4 ?$$

x uchun yechish

$$x=\frac{2}{5}=0,4$$

$$x=-\frac{2}{5}=-0,4$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 25 ga bo‘ling.

$$x^{2}=\frac{4}{25}$$

Ikkala tarafdan \frac{4}{25} ni ayirish.

$$x^{2}-\frac{4}{25}=0$$

Ikkala tarafini 25 ga ko‘paytiring.

$$25x^{2}-4=0$$

Hisoblang: 25x^{2}-4. 25x^{2}-4 ni \left(5x\right)^{2}-2^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5x-2\right)\left(5x+2\right)=0$$

Tenglamani yechish uchun 5x-2=0 va 5x+2=0 ni yeching.

$$x=\frac{2}{5} x=-\frac{2}{5}$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikki tarafini 25 ga bo‘ling.

$$x^{2}=\frac{4}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{2}{5} x=-\frac{2}{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 25 ga bo‘ling.

$$x^{2}=\frac{4}{25}$$

Ikkala tarafdan \frac{4}{25} ni ayirish.

$$x^{2}-\frac{4}{25}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -\frac{4}{25} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{4}{25}\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-\frac{4}{25}\right)}}{2}$$

-4 ni -\frac{4}{25} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{\frac{16}{25}}}{2}$$

\frac{16}{25} ning kvadrat ildizini chiqarish.

$$x=\frac{0±\frac{4}{5}}{2}$$

x=\frac{0±\frac{4}{5}}{2} tenglamasini yeching, bunda ± musbat.

$$x=\frac{2}{5}$$

x=\frac{0±\frac{4}{5}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{2}{5}$$

Tenglama yechildi.

$$x=\frac{2}{5} x=-\frac{2}{5}$$