144q^2=25 eching

$$144 q ^ { 2 } = 25$$

q uchun yechish

$$q=\frac{5}{12}\approx 0,416666667$$

$$q=-\frac{5}{12}\approx -0,416666667$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 144 ga bo‘ling.

$$q^{2}=\frac{25}{144}$$

Ikkala tarafdan \frac{25}{144} ni ayirish.

$$q^{2}-\frac{25}{144}=0$$

Ikkala tarafini 144 ga ko‘paytiring.

$$144q^{2}-25=0$$

Hisoblang: 144q^{2}-25. 144q^{2}-25 ni \left(12q\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).

$$\left(12q-5\right)\left(12q+5\right)=0$$

Tenglamani yechish uchun 12q-5=0 va 12q+5=0 ni yeching.

$$q=\frac{5}{12} q=-\frac{5}{12}$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikki tarafini 144 ga bo‘ling.

$$q^{2}=\frac{25}{144}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$q=\frac{5}{12} q=-\frac{5}{12}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 144 ga bo‘ling.

$$q^{2}=\frac{25}{144}$$

Ikkala tarafdan \frac{25}{144} ni ayirish.

$$q^{2}-\frac{25}{144}=0$$

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}{144} ni c bilan almashtiring.

$$q=\frac{0±\sqrt{0^{2}-4\left(-\frac{25}{144}\right)}}{2}$$

0 kvadratini chiqarish.

$$q=\frac{0±\sqrt{-4\left(-\frac{25}{144}\right)}}{2}$$

-4 ni -\frac{25}{144} marotabaga ko'paytirish.

$$q=\frac{0±\sqrt{\frac{25}{36}}}{2}$$

\frac{25}{36} ning kvadrat ildizini chiqarish.

$$q=\frac{0±\frac{5}{6}}{2}$$

q=\frac{0±\frac{5}{6}}{2} tenglamasini yeching, bunda ± musbat.

$$q=\frac{5}{12}$$

q=\frac{0±\frac{5}{6}}{2} tenglamasini yeching, bunda ± manfiy.

$$q=-\frac{5}{12}$$

Tenglama yechildi.

$$q=\frac{5}{12} q=-\frac{5}{12}$$