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

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

A uchun yechish

$$A=\frac{2738}{n^{2}}$$

$$n\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$An^{2}=2\left(11^{2}-107^{2}\right)+2\times 96^{2}+2\times 59^{2}$$

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

$$An^{2}=2\left(121-107^{2}\right)+2\times 96^{2}+2\times 59^{2}$$

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

$$An^{2}=2\left(121-11449\right)+2\times 96^{2}+2\times 59^{2}$$

-11328 olish uchun 121 dan 11449 ni ayirish.

$$An^{2}=2\left(-11328\right)+2\times 96^{2}+2\times 59^{2}$$

-22656 hosil qilish uchun 2 va -11328 ni ko'paytirish.

$$An^{2}=-22656+2\times 96^{2}+2\times 59^{2}$$

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

$$An^{2}=-22656+2\times 9216+2\times 59^{2}$$

18432 hosil qilish uchun 2 va 9216 ni ko'paytirish.

$$An^{2}=-22656+18432+2\times 59^{2}$$

-4224 olish uchun -22656 va 18432'ni qo'shing.

$$An^{2}=-4224+2\times 59^{2}$$

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

$$An^{2}=-4224+2\times 3481$$

6962 hosil qilish uchun 2 va 3481 ni ko'paytirish.

$$An^{2}=-4224+6962$$

2738 olish uchun -4224 va 6962'ni qo'shing.

$$An^{2}=2738$$

Tenglama standart shaklda.

$$n^{2}A=2738$$

Ikki tarafini n^{2} ga bo‘ling.

$$\frac{n^{2}A}{n^{2}}=\frac{2738}{n^{2}}$$

n^{2} ga bo'lish n^{2} ga ko'paytirishni bekor qiladi.

$$A=\frac{2738}{n^{2}}$$

n uchun yechish (complex solution)

$$n=-37\sqrt{2}A^{-\frac{1}{2}}$$

$$n=37\sqrt{2}A^{-\frac{1}{2}}\text{, }A\neq 0$$

n uchun yechish

$$n=37\sqrt{\frac{2}{A}}$$

$$n=-37\sqrt{\frac{2}{A}}\text{, }A>0$$