Question

If 2^x = 3^y = 6^z then show that, xy + yz + zx =0
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Answer 1

Answer:

HOPE IT'S HELPFUL...............

Answer 2

${2}^{x} = {3}^{y} = {6}^{z} = k \: (say)$

=> $2 = {k}^{1 \div x}$

=> $3 = {k}^{1 \div y}$

=> $6 = {k}^{1 \div z}$

Now, 6 = 3×2

=> ${k}^{1 \div z} = {k}^{1 \div y} \times {k}^{1 \div x}$

=> $\frac{1}{z} = \frac{y + x}{xy}$

=> $xy - yz - xz = 0$