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Cube Numbers

If x=log_cb +...

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If x=\log{}_cb +\log{}_bc, y=\log{}_ac +log{}_ca and z=\log{}_ba +\log{}_ab, then x^2 +y^2 +z^2 is equal to (A) 1 (B) 2 (C) xyz (D) xyz +4

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Q. Prove that if x =

l o g_{c} b + l o g_{b} c

y = l o g_{a} c + l o g_{c} a,

z = l o g_{b} a + l o g_{a} b

x y z = x^{2} + y^{2} + z^{2} - 4.

Q. The value of the expression

\frac{1}{1 + {log}_{b} a + {log}_{b} c} + \frac{1}{1 + {log}_{c} a + {log}_{c} b} + \frac{1}{1 + {log}_{a} b + {log}_{a} c}

Q. Find the value of

\frac{1}{1 + {log}_{b} a + {log}_{b} c} + \frac{1}{1 + {log}_{c} a + {log}_{c} b} + \frac{1}{1 + {log}_{a} b + {log}_{a} c}

.

{log}_{b} a + {log}_{c} a + {log}_{a} b + {log}_{a} c + {log}_{b} c + {log}_{c} b = 3

a, b, c

are different positive real numbers

\neq 1

), then find the value of

a b c

x = l o g_{b} a, y = l o g_{c} b, z = l o g_{a} c

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