If x, z, y, a, b, c are real and non is zero xy=a xz=b yz=c then x square +y square +z square=_

Dear Bharat
I think the question should be the to find the value of  x² – y² + z²
please check and repost the question
Regards
Arun (askIITians forum expert)

Sorry, I got your question
xy = a           …....(i)
xz = b          …....(ii)
yz = c         …......(iii)
now  multiply (i) and (ii)
x²yz = ab
similarly
xy²z = ac
xyz² = bc
now x² = ab/yz = ab/c
similarly
y² = ac / xz = ac/b
z² = bc/ xy = bc / a
hence
x² +  y² + z² = ab/c + ac/b +  bc/a
Regards
Arun (askIITians forum expert)