a^2=25/121 eching

$$a ^ { 2 } = \frac { 25 } { 121 }$$

a uchun yechish

$$a=\frac{5}{11}\approx 0,454545455$$

$$a=-\frac{5}{11}\approx -0,454545455$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan \frac{25}{121} ni ayirish.

$$a^{2}-\frac{25}{121}=0$$

Ikkala tarafini 121 ga ko‘paytiring.

$$121a^{2}-25=0$$

Hisoblang: 121a^{2}-25. 121a^{2}-25 ni \left(11a\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).

$$\left(11a-5\right)\left(11a+5\right)=0$$

Tenglamani yechish uchun 11a-5=0 va 11a+5=0 ni yeching.

$$a=\frac{5}{11} a=-\frac{5}{11}$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$a=\frac{5}{11} a=-\frac{5}{11}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan \frac{25}{121} ni ayirish.

$$a^{2}-\frac{25}{121}=0$$

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}{121} ni c bilan almashtiring.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{25}{121}\right)}}{2}$$

0 kvadratini chiqarish.

$$a=\frac{0±\sqrt{-4\left(-\frac{25}{121}\right)}}{2}$$

-4 ni -\frac{25}{121} marotabaga ko'paytirish.

$$a=\frac{0±\sqrt{\frac{100}{121}}}{2}$$

\frac{100}{121} ning kvadrat ildizini chiqarish.

$$a=\frac{0±\frac{10}{11}}{2}$$

a=\frac{0±\frac{10}{11}}{2} tenglamasini yeching, bunda ± musbat.

$$a=\frac{5}{11}$$

a=\frac{0±\frac{10}{11}}{2} tenglamasini yeching, bunda ± manfiy.

$$a=-\frac{5}{11}$$

Tenglama yechildi.

$$a=\frac{5}{11} a=-\frac{5}{11}$$