If x(x+y+z)=9,y(x+y+z)=16 and z(x+y+z)=144, then x=?

• x=9/13,-9/13.
  sol:-
  adding all equations after that we will get
  (x+y+z)^2=169
  x+y+z=13,-13
  after putting these values in eq-n number one we get
  x=-9/13,9/13 ans.
• 12 years agoHelpfull: Yes(20) No(2)
• let x+y+z=k
  
  x(x+y+z)=9 can be written as xk=9
  similarly yk=16
  also zk=144
  ---------------------------------------
  add these k(x+y+z)=169
  or k.k=169 (bcoz x+y+z=k assumed)
  ie k^2=13^2
  k=+13,-13
  
  hence from the first eqn x(x+y+z)=9
  x.k=9
  x=9/k
  
  or x=9/13 or -9/13
• 12 years agoHelpfull: Yes(15) No(0)
• x=9/13
  y=16/13
  z=144/13
  reason: x+y+z=9/x=16/y=144/z
  x:y:z=9:16:144
  
  x(x+16x/9+144x/9)=9
  solving x=9/13
  so y=16/13 and z=144/13
• 12 years agoHelpfull: Yes(3) No(9)
• x(x+y+z)=9 equation named as 1
  y(x+y+z)=16 equation named as 2
  z(x+y+z)=144 equation named as 3
  
  let (x+y+z) as A
  then sum of this equtions 1,2 and 3 becomes
  (A)*A=169
  A^2=169 then A=13,
  from equation 1
  x*A=9
  therfore x=(9/A)
  ans is x=(9/13).
  
  
• 12 years agoHelpfull: Yes(3) No(0)
• x=9/x+y+z..............>(1)
  y=16/x+y+z
  2=144/x+y+z
  x+y+z=(9/x+y+z)+(16/x+y+z)+(144/x+y+z)
  x+y+z=169/x+y+z
  (x+y+z)2=13*13
  x+y+z=13
  from 1
  x=9/13
• 11 years agoHelpfull: Yes(2) No(0)
• Answer is 9/13.
  because if we add all these equations then,
  x(x+y+z)+y(x+y+z)+z(x+y+z)=9+16+144
  & (x+y+z)(x+y+z) = 169
  (x+y+z) = 13
  therefore x=9/13
• 11 years agoHelpfull: Yes(0) No(0)
• x=9/13
  y=16/13
  z=144/13
  
  
  adding all three equation, we get,
  (x+y+z)(x+y+z)=169
  (x+y+z)sq 2=13 sq 2
  (x+y+z)=13
  
  
• 11 years agoHelpfull: Yes(0) No(0)
• x(x+y+z)+y(x+y+z)+z(x+y+z)=9+16+144
  now, taking common (x+y+z) in L.H.S
  (x+y+z)(x+y+z)=169
  (x+y+z)=+-13
  x=+9/13,-9/13
• 11 years agoHelpfull: Yes(0) No(0)
• add all three equations
  we get
  (x+y+z)^2=169
  x+y+z=13
  put it in equation 1
  x=9/13
  
• 10 years agoHelpfull: Yes(0) No(0)
• x= 9/13, just divide then replace the value of y and z in terms of x
• 8 years agoHelpfull: Yes(0) No(0)