xyz+x+y+z+xy+xz+yz=1989 eching

$$xyz+x+y+z+xy+xz+yz=1989$$

x uchun yechish

$$x=-\frac{yz+y+z-1989}{yz+y+z+1}$$

$$z\neq -1\text{ and }y\neq -1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan y ni ayirish.

$$xyz+x+z+xy+xz+yz=1989-y$$

Ikkala tarafdan z ni ayirish.

$$xyz+x+xy+xz+yz=1989-y-z$$

Ikkala tarafdan yz ni ayirish.

$$xyz+x+xy+xz=1989-y-z-yz$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(yz+1+y+z\right)x=1989-y-z-yz$$

Tenglama standart shaklda.

$$\left(yz+y+z+1\right)x=1989-z-y-yz$$

Ikki tarafini yz+1+y+z ga bo‘ling.

$$\frac{\left(yz+y+z+1\right)x}{yz+y+z+1}=\frac{1989-z-y-yz}{yz+y+z+1}$$

yz+1+y+z ga bo'lish yz+1+y+z ga ko'paytirishni bekor qiladi.

$$x=\frac{1989-z-y-yz}{yz+y+z+1}$$

y uchun yechish

$$y=-\frac{xz+x+z-1989}{xz+x+z+1}$$

$$z\neq -1\text{ and }x\neq -1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan x ni ayirish.

$$xyz+y+z+xy+xz+yz=1989-x$$

Ikkala tarafdan z ni ayirish.

$$xyz+y+xy+xz+yz=1989-x-z$$

Ikkala tarafdan xz ni ayirish.

$$xyz+y+xy+yz=1989-x-z-xz$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(xz+1+x+z\right)y=1989-x-z-xz$$

Tenglama standart shaklda.

$$\left(xz+x+z+1\right)y=1989-z-x-xz$$

Ikki tarafini xz+1+x+z ga bo‘ling.

$$\frac{\left(xz+x+z+1\right)y}{xz+x+z+1}=\frac{1989-z-x-xz}{xz+x+z+1}$$

xz+1+x+z ga bo'lish xz+1+x+z ga ko'paytirishni bekor qiladi.

$$y=\frac{1989-z-x-xz}{xz+x+z+1}$$