Question

Giai he phuong trinh:

a) \(\hept{\begin{cases}\left(x+y\right).\left(y+z\right)=187\\\left(y+z\right).\left(z+x\right)=154\\\left(z+x\right).\left(x+y\right)=238\end{cases}}\)

b) \(\hept{\begin{cases}x^2-y^2=1\\4x^2-5xy=2\end{cases}}\)

Answer 1

\(Taco:\)

\(\left(x+y\right)\left(y+z\right)=187\Leftrightarrow xy+xz+yy+yz=187\)

\(\left(y+z\right)\left(z+x\right)=154\Leftrightarrow yz+xy+zz+xz=154\)

\(\left(z+x\right)\left(x+y\right)=238\Leftrightarrow xz+zy+xx+xy=238\)

\(\Rightarrow\left(x+y\right)\left(y+z\right)+\left(x+z\right)\left(x+y\right)+\left(y+z\right)\left(z+x\right)=579\)

\(\Leftrightarrow xy+zx+yy+yz+yz+xy+zz+xz+xz+zy+xx+xy=579\)

\(\Leftrightarrow3\left(xz+xy+yz\right)+x^2+y^2+z^2=579\)

\(\left(z+x\right)\left(x+y\right)-\left(x+y\right)\left(y+z\right)=51\)

\(\Leftrightarrow\left(x+y\right)\left(x-y\right)=x^2-y^2=51\)

\(\left(z+x\right)\left(x+y\right)-\left(y+z\right)\left(x+z\right)=84\)

\(\Leftrightarrow\left(x+z\right)\left(x-z\right)=84\Leftrightarrow x^2-z^2=84\)

\(\Leftrightarrow y^2-z^2=33\)

đến đây tịt

Answer 2

ak tớ bt cách giải rồi cần thì ib ns tớ lm :v