Solve the given system of quadratic equations \(\displaystyle{x}^{{2}}+{x}{y}+{x}{z}={2}\)

Octavio Chen

Octavio Chen

Answered question

2022-03-22

Solve the given system of quadratic equations
x2+xy+xz=2
y2+yz+xy=3
z2+zx+yz=4

Answer & Explanation

memantangti17

memantangti17

Beginner2022-03-23Added 13 answers

Your equations are equivalent to
x(x+y+z)=2, y(x+y+z)=3, z(x+y+z)=4.
Set x+y+z=t,
that t2=2+3+4=9 and we have t=±3. Hence
x=±d23,    y=±1,    z=±d43.
Edit: Btw, here we hove only two solutions for the system.

aznluck4u72x4

aznluck4u72x4

Beginner2022-03-24Added 16 answers

Take x=2t    y=3t    z=4t;
We know this is valid because x+y+z must be nonzero, so too the individual letters, and
yx=32    zx=42;
Then x+y+z=9t

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