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

Answer 1

(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

Answer 2

(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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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).

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).