Question

If (x + y)2 – z 2 = 4, (y + z)2 – x 2 = 9 and (z + x)2 – y 2 = 36, then find the value of x + y + z

Answer 1

(x+y)^2 - z^2 = 4
=> x^2 + y^2 - z^2 + 2xy = 4. (1)

(y+z)^2 - x^2 = 9
=> y^2 + z^2 - x^2 + 2yz = 9. (2)

(z+x)^2 - y^2 = 36
=> z^2 + x^2 - y^2 + 2xz = 36. (3)

Adding (1), (2) and (3)

x^2 + y^2 + z^2 + 2xy + 2yz + 2xz = 49
=> (x+y+z)^2 = (7)^2
=> x+y+z = 7

Hope this helps... plsss make it the brainliest