{x^{2}=9^{2}+6^{2}+7^{2}+4^{2}+3^{2}+3^2+2^2+5^2+2^2 eching

$$\{ x ^ { 2 } = 9 ^ { 2 } + 6 ^ { 2 } + 7 ^ { 2 } + 4 ^ { 2 } + 3 ^ { 2 } + 3 ^ { 2 } + 2 ^ { 2 } + 5 ^ { 2 } + 2 ^ { 2 }$$

x uchun yechish

$$x=\sqrt{233}\approx 15,264337522$$

$$x=-\sqrt{233}\approx -15,264337522$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

$$x^{2}=81+6^{2}+7^{2}+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 6 ga hisoblang va 36 ni qiymatni oling.

$$x^{2}=81+36+7^{2}+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

117 olish uchun 81 va 36'ni qo'shing.

$$x^{2}=117+7^{2}+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$x^{2}=117+49+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

166 olish uchun 117 va 49'ni qo'shing.

$$x^{2}=166+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$x^{2}=166+16+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

182 olish uchun 166 va 16'ni qo'shing.

$$x^{2}=182+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$x^{2}=182+9+3^{2}+2^{2}+5^{2}+2^{2}$$

191 olish uchun 182 va 9'ni qo'shing.

$$x^{2}=191+3^{2}+2^{2}+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$x^{2}=191+9+2^{2}+5^{2}+2^{2}$$

200 olish uchun 191 va 9'ni qo'shing.

$$x^{2}=200+2^{2}+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$x^{2}=200+4+5^{2}+2^{2}$$

204 olish uchun 200 va 4'ni qo'shing.

$$x^{2}=204+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$x^{2}=204+25+2^{2}$$

229 olish uchun 204 va 25'ni qo'shing.

$$x^{2}=229+2^{2}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$x^{2}=229+4$$

233 olish uchun 229 va 4'ni qo'shing.

$$x^{2}=233$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{233} x=-\sqrt{233}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 9 ga hisoblang va 81 ni qiymatni oling.

$$x^{2}=81+6^{2}+7^{2}+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 6 ga hisoblang va 36 ni qiymatni oling.

$$x^{2}=81+36+7^{2}+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

117 olish uchun 81 va 36'ni qo'shing.

$$x^{2}=117+7^{2}+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$x^{2}=117+49+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

166 olish uchun 117 va 49'ni qo'shing.

$$x^{2}=166+4^{2}+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$x^{2}=166+16+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

182 olish uchun 166 va 16'ni qo'shing.

$$x^{2}=182+3^{2}+3^{2}+2^{2}+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$x^{2}=182+9+3^{2}+2^{2}+5^{2}+2^{2}$$

191 olish uchun 182 va 9'ni qo'shing.

$$x^{2}=191+3^{2}+2^{2}+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$x^{2}=191+9+2^{2}+5^{2}+2^{2}$$

200 olish uchun 191 va 9'ni qo'shing.

$$x^{2}=200+2^{2}+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$x^{2}=200+4+5^{2}+2^{2}$$

204 olish uchun 200 va 4'ni qo'shing.

$$x^{2}=204+5^{2}+2^{2}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$x^{2}=204+25+2^{2}$$

229 olish uchun 204 va 25'ni qo'shing.

$$x^{2}=229+2^{2}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$x^{2}=229+4$$

233 olish uchun 229 va 4'ni qo'shing.

$$x^{2}=233$$

Ikkala tarafdan 233 ni ayirish.

$$x^{2}-233=0$$

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 -233 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-233\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-233\right)}}{2}$$

-4 ni -233 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{932}}{2}$$

932 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{233}}{2}$$

x=\frac{0±2\sqrt{233}}{2} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{233}$$

x=\frac{0±2\sqrt{233}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{233}$$

Tenglama yechildi.

$$x=\sqrt{233} x=-\sqrt{233}$$