100^2+100+8=3p^2-190+11 eching

$$100 ^ { 2 } + 100 + 8 = 3 p ^ { 2 } - 190 + 11$$

p uchun yechish

$$p=3\sqrt{381}\approx 58,557663888$$

$$p=-3\sqrt{381}\approx -58,557663888$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 100 ga hisoblang va 10000 ni qiymatni oling.

$$10000+100+8=3p^{2}-190+11$$

10100 olish uchun 10000 va 100'ni qo'shing.

$$10100+8=3p^{2}-190+11$$

10108 olish uchun 10100 va 8'ni qo'shing.

$$10108=3p^{2}-190+11$$

-179 olish uchun -190 va 11'ni qo'shing.

$$10108=3p^{2}-179$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$3p^{2}-179=10108$$

179 ni ikki tarafga qo’shing.

$$3p^{2}=10108+179$$

10287 olish uchun 10108 va 179'ni qo'shing.

$$3p^{2}=10287$$

Ikki tarafini 3 ga bo‘ling.

$$p^{2}=\frac{10287}{3}$$

3429 ni olish uchun 10287 ni 3 ga bo‘ling.

$$p^{2}=3429$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$p=3\sqrt{381} p=-3\sqrt{381}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 100 ga hisoblang va 10000 ni qiymatni oling.

$$10000+100+8=3p^{2}-190+11$$

10100 olish uchun 10000 va 100'ni qo'shing.

$$10100+8=3p^{2}-190+11$$

10108 olish uchun 10100 va 8'ni qo'shing.

$$10108=3p^{2}-190+11$$

-179 olish uchun -190 va 11'ni qo'shing.

$$10108=3p^{2}-179$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$3p^{2}-179=10108$$

Ikkala tarafdan 10108 ni ayirish.

$$3p^{2}-179-10108=0$$

-10287 olish uchun -179 dan 10108 ni ayirish.

$$3p^{2}-10287=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 0 ni b va -10287 ni c bilan almashtiring.

$$p=\frac{0±\sqrt{0^{2}-4\times 3\left(-10287\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$p=\frac{0±\sqrt{-4\times 3\left(-10287\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$p=\frac{0±\sqrt{-12\left(-10287\right)}}{2\times 3}$$

-12 ni -10287 marotabaga ko'paytirish.

$$p=\frac{0±\sqrt{123444}}{2\times 3}$$

123444 ning kvadrat ildizini chiqarish.

$$p=\frac{0±18\sqrt{381}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$p=\frac{0±18\sqrt{381}}{6}$$

p=\frac{0±18\sqrt{381}}{6} tenglamasini yeching, bunda ± musbat.

$$p=3\sqrt{381}$$

p=\frac{0±18\sqrt{381}}{6} tenglamasini yeching, bunda ± manfiy.

$$p=-3\sqrt{381}$$

Tenglama yechildi.

$$p=3\sqrt{381} p=-3\sqrt{381}$$