/n^2=11^2-107^2+96^2+{59}^2 eching

$$\frac{ }{ } { n }^{ 2 } = { 11 }^{ 2 } - { 107 }^{ 2 } + { 96 }^{ 2 } + { 59 }^{ 2 }$$

n uchun yechish

$$n=-37$$

$$n=37$$

Kvadratlar farqidan foydalangan qadamlar

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$1n^{2}=11^{2}-107^{2}+96^{2}+59^{2}$$

2 daraja ko‘rsatkichini 11 ga hisoblang va 121 ni qiymatni oling.

$$1n^{2}=121-107^{2}+96^{2}+59^{2}$$

2 daraja ko‘rsatkichini 107 ga hisoblang va 11449 ni qiymatni oling.

$$1n^{2}=121-11449+96^{2}+59^{2}$$

-11328 olish uchun 121 dan 11449 ni ayirish.

$$1n^{2}=-11328+96^{2}+59^{2}$$

2 daraja ko‘rsatkichini 96 ga hisoblang va 9216 ni qiymatni oling.

$$1n^{2}=-11328+9216+59^{2}$$

-2112 olish uchun -11328 va 9216'ni qo'shing.

$$1n^{2}=-2112+59^{2}$$

2 daraja ko‘rsatkichini 59 ga hisoblang va 3481 ni qiymatni oling.

$$1n^{2}=-2112+3481$$

1369 olish uchun -2112 va 3481'ni qo'shing.

$$1n^{2}=1369$$

Ikkala tarafdan 1369 ni ayirish.

$$1n^{2}-1369=0$$

Shartlarni qayta saralash.

$$n^{2}-1369=0$$

Hisoblang: n^{2}-1369. n^{2}-1369 ni n^{2}-37^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(n-37\right)\left(n+37\right)=0$$

Tenglamani yechish uchun n-37=0 va n+37=0 ni yeching.

$$n=37 n=-37$$

Kvadrat ildizini topish bo'yicha qadamlar

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$1n^{2}=11^{2}-107^{2}+96^{2}+59^{2}$$

2 daraja ko‘rsatkichini 11 ga hisoblang va 121 ni qiymatni oling.

$$1n^{2}=121-107^{2}+96^{2}+59^{2}$$

2 daraja ko‘rsatkichini 107 ga hisoblang va 11449 ni qiymatni oling.

$$1n^{2}=121-11449+96^{2}+59^{2}$$

-11328 olish uchun 121 dan 11449 ni ayirish.

$$1n^{2}=-11328+96^{2}+59^{2}$$

2 daraja ko‘rsatkichini 96 ga hisoblang va 9216 ni qiymatni oling.

$$1n^{2}=-11328+9216+59^{2}$$

-2112 olish uchun -11328 va 9216'ni qo'shing.

$$1n^{2}=-2112+59^{2}$$

2 daraja ko‘rsatkichini 59 ga hisoblang va 3481 ni qiymatni oling.

$$1n^{2}=-2112+3481$$

1369 olish uchun -2112 va 3481'ni qo'shing.

$$1n^{2}=1369$$

Ikki tarafini 1 ga bo‘ling.

$$n^{2}=1369$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$n=37 n=-37$$

Kvadrat tenglamalaridan foydalanish qoidalari

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$1n^{2}=11^{2}-107^{2}+96^{2}+59^{2}$$

2 daraja ko‘rsatkichini 11 ga hisoblang va 121 ni qiymatni oling.

$$1n^{2}=121-107^{2}+96^{2}+59^{2}$$

2 daraja ko‘rsatkichini 107 ga hisoblang va 11449 ni qiymatni oling.

$$1n^{2}=121-11449+96^{2}+59^{2}$$

-11328 olish uchun 121 dan 11449 ni ayirish.

$$1n^{2}=-11328+96^{2}+59^{2}$$

2 daraja ko‘rsatkichini 96 ga hisoblang va 9216 ni qiymatni oling.

$$1n^{2}=-11328+9216+59^{2}$$

-2112 olish uchun -11328 va 9216'ni qo'shing.

$$1n^{2}=-2112+59^{2}$$

2 daraja ko‘rsatkichini 59 ga hisoblang va 3481 ni qiymatni oling.

$$1n^{2}=-2112+3481$$

1369 olish uchun -2112 va 3481'ni qo'shing.

$$1n^{2}=1369$$

Ikkala tarafdan 1369 ni ayirish.

$$1n^{2}-1369=0$$

Shartlarni qayta saralash.

$$n^{2}-1369=0$$

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 -1369 ni c bilan almashtiring.

$$n=\frac{0±\sqrt{0^{2}-4\left(-1369\right)}}{2}$$

0 kvadratini chiqarish.

$$n=\frac{0±\sqrt{-4\left(-1369\right)}}{2}$$

-4 ni -1369 marotabaga ko'paytirish.

$$n=\frac{0±\sqrt{5476}}{2}$$

5476 ning kvadrat ildizini chiqarish.

$$n=\frac{0±74}{2}$$

n=\frac{0±74}{2} tenglamasini yeching, bunda ± musbat. 74 ni 2 ga bo'lish.

$$n=37$$

n=\frac{0±74}{2} tenglamasini yeching, bunda ± manfiy. -74 ni 2 ga bo'lish.

$$n=-37$$

Tenglama yechildi.

$$n=37 n=-37$$