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Question

If ax^(-1) = bc, by^(-1) = ac, cz ^(-1) = ab such that x, y, z are integers then value of xy + yz + zx – xyz is


Solution

a^x / a = bc , a^x = abc

b^y / b = ca , b^y = abc

c^z / c = ab . c^z = abc

a = (abc)^1/x

b = (abc)^1/y

c = (abc)^1/z

abc = (abc)^(1/x+1/y+1/z) 

(abc)^1 = (abc)^(1/x+1/y+1/z) 

1/x+1/y+1/z = 1

(xy + yz + zx) / xyz = 1

xy + yz + zx = xyz
so  XY + YZ + ZX - XYZ = 0

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