81x^2=25 eching

$$81 x ^ { 2 } = 25$$

x uchun yechish

$$x=\frac{5}{9}\approx 0,555555556$$

$$x=-\frac{5}{9}\approx -0,555555556$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 81 ga bo‘ling.

$$x^{2}=\frac{25}{81}$$

Ikkala tarafdan \frac{25}{81} ni ayirish.

$$x^{2}-\frac{25}{81}=0$$

Ikkala tarafini 81 ga ko‘paytiring.

$$81x^{2}-25=0$$

Hisoblang: 81x^{2}-25. 81x^{2}-25 ni \left(9x\right)^{2}-5^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(9x-5\right)\left(9x+5\right)=0$$

Tenglamani yechish uchun 9x-5=0 va 9x+5=0 ni yeching.

$$x=\frac{5}{9} x=-\frac{5}{9}$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikki tarafini 81 ga bo‘ling.

$$x^{2}=\frac{25}{81}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{5}{9} x=-\frac{5}{9}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 81 ga bo‘ling.

$$x^{2}=\frac{25}{81}$$

Ikkala tarafdan \frac{25}{81} ni ayirish.

$$x^{2}-\frac{25}{81}=0$$

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{25}{81} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{25}{81}\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-\frac{25}{81}\right)}}{2}$$

-4 ni -\frac{25}{81} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{\frac{100}{81}}}{2}$$

\frac{100}{81} ning kvadrat ildizini chiqarish.

$$x=\frac{0±\frac{10}{9}}{2}$$

x=\frac{0±\frac{10}{9}}{2} tenglamasini yeching, bunda ± musbat.

$$x=\frac{5}{9}$$

x=\frac{0±\frac{10}{9}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{5}{9}$$

Tenglama yechildi.

$$x=\frac{5}{9} x=-\frac{5}{9}$$