9p^2=49 eching

$$9 p ^ { 2 } = 49$$

p uchun yechish

$$p = \frac{7}{3} = 2\frac{1}{3} \approx 2,333333333$$

$$p = -\frac{7}{3} = -2\frac{1}{3} \approx -2,333333333$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 9 ga bo‘ling.

$$p^{2}=\frac{49}{9}$$

Ikkala tarafdan \frac{49}{9} ni ayirish.

$$p^{2}-\frac{49}{9}=0$$

Ikkala tarafini 9 ga ko‘paytiring.

$$9p^{2}-49=0$$

Hisoblang: 9p^{2}-49. 9p^{2}-49 ni \left(3p\right)^{2}-7^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3p-7\right)\left(3p+7\right)=0$$

Tenglamani yechish uchun 3p-7=0 va 3p+7=0 ni yeching.

$$p=\frac{7}{3} p=-\frac{7}{3}$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikki tarafini 9 ga bo‘ling.

$$p^{2}=\frac{49}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$p=\frac{7}{3} p=-\frac{7}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 9 ga bo‘ling.

$$p^{2}=\frac{49}{9}$$

Ikkala tarafdan \frac{49}{9} ni ayirish.

$$p^{2}-\frac{49}{9}=0$$

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{49}{9} ni c bilan almashtiring.

$$p=\frac{0±\sqrt{0^{2}-4\left(-\frac{49}{9}\right)}}{2}$$

0 kvadratini chiqarish.

$$p=\frac{0±\sqrt{-4\left(-\frac{49}{9}\right)}}{2}$$

-4 ni -\frac{49}{9} marotabaga ko'paytirish.

$$p=\frac{0±\sqrt{\frac{196}{9}}}{2}$$

\frac{196}{9} ning kvadrat ildizini chiqarish.

$$p=\frac{0±\frac{14}{3}}{2}$$

p=\frac{0±\frac{14}{3}}{2} tenglamasini yeching, bunda ± musbat.

$$p=\frac{7}{3}$$

p=\frac{0±\frac{14}{3}}{2} tenglamasini yeching, bunda ± manfiy.

$$p=-\frac{7}{3}$$

Tenglama yechildi.

$$p=\frac{7}{3} p=-\frac{7}{3}$$