a+b+c+abc=25 eching

$$a+b+c+abc=25$$

a uchun yechish

$$\left\{\begin{matrix}a=-\frac{b+c-25}{bc+1}\text{, }&c=0\text{ or }b\neq -\frac{1}{c}\\a\in \mathrm{R}\text{, }&\left(b=\frac{\sqrt{629}+25}{2}\text{ and }c=\frac{25-\sqrt{629}}{2}\right)\text{ or }\left(b=\frac{25-\sqrt{629}}{2}\text{ and }c=\frac{\sqrt{629}+25}{2}\right)\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan b ni ayirish.

$$a+c+abc=25-b$$

Ikkala tarafdan c ni ayirish.

$$a+abc=25-b-c$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(1+bc\right)a=25-b-c$$

Tenglama standart shaklda.

$$\left(bc+1\right)a=25-c-b$$

Ikki tarafini 1+bc ga bo‘ling.

$$\frac{\left(bc+1\right)a}{bc+1}=\frac{25-c-b}{bc+1}$$

1+bc ga bo'lish 1+bc ga ko'paytirishni bekor qiladi.

$$a=\frac{25-c-b}{bc+1}$$

b uchun yechish

$$\left\{\begin{matrix}b=-\frac{a+c-25}{ac+1}\text{, }&c=0\text{ or }a\neq -\frac{1}{c}\\b\in \mathrm{R}\text{, }&\left(a=\frac{\sqrt{629}+25}{2}\text{ and }c=\frac{25-\sqrt{629}}{2}\right)\text{ or }\left(a=\frac{25-\sqrt{629}}{2}\text{ and }c=\frac{\sqrt{629}+25}{2}\right)\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan a ni ayirish.

$$b+c+abc=25-a$$

Ikkala tarafdan c ni ayirish.

$$b+abc=25-a-c$$

b'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(1+ac\right)b=25-a-c$$

Tenglama standart shaklda.

$$\left(ac+1\right)b=25-c-a$$

Ikki tarafini 1+ac ga bo‘ling.

$$\frac{\left(ac+1\right)b}{ac+1}=\frac{25-c-a}{ac+1}$$

1+ac ga bo'lish 1+ac ga ko'paytirishni bekor qiladi.

$$b=\frac{25-c-a}{ac+1}$$