If $\frac{{\log x}}{{{a^2} + ab + {b^2}}} = \frac{{{\rm{log}}y}}{{{b^2} + bc + {c^2}}} = \frac{{\log z}}{{{c^2} + ca + {a^2}}},$ then ${x^{a - b}}.{y^{b - c}}.{z^{c - a}} = $

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

\frac{{\log x}}{{{a^2} + ab + {b^2}}} = \frac{{\mathrm{log}y}}{{{b^2} + bc + {c^2}}} = \frac{{\log z}}{{{c^2} + ca + {a^2}}},

then

{x^{a - b}}.{y^{b - c}}.{z^{c - a}} =

View answer and explanation

Correct option: C

Option C (1) is correct because when the given ratios are manipulated and combined using logarithm properties, the result simplifies to 1.

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