if (x+y)^2 – z^2 = 8,. (y+z)^2 – x^2 = 10 and

(x+z)^2 – y^2 = 7,. then find the value of

(x+y+z).

Question

if (x+y)^2 – z^2 = 8,.      (y+z)^2 – x^2 = 10 and
   
   (x+z)^2 – y^2 = 7,.    then find the value of

(x+y+z).

Hemant Kumar Mudgal · Answer

(x+y)2 = 8+z2 
(y+z)2 = 10 + x2 
(X+z)2 = 7 + y2

adding all equations

2 x2 + 2 y2 + 2z2 + 2xy + 2zx +2yz = x2 + y2 + z2 + 25

after solutioning this eq 
 
then we have

(X+y+z+)2 = 25 
X+y+z = 5

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