Question

If x^a = y^b = z^c & ab+ bc+ ac = 0 , prove that xyz = 1

Answer 1

Answer:

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Answer 2

Answer:

This is an interesting problem. Here is one observation.

a^x = b^y = c^z

Hence

a = c^z/x and b = c^z/y

Hence ab = (c^1/x.c^1/y)^z

Hence ab = c^z(1/x + 1/y) = c^(z(x + y)/xy) = c^(z^2)(x + y)

Similarly bc = a^(x^2)(y + z) and ca = b^(y^2)(z + x)

Hence ab + bc + ca = c^(z^2)(x + y) + a^(x^2)(y + z) + b^(y^2)(z + x)

Step-by-step explanation:

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