Question

If a^x=b^y=c^z and b^2=ac prove that y=2xz/x+z​

Answer 1

Answer:

y=2xz / x+z​

Step-by-step explanation:

           $a^x = b^y => a = b^{\frac {y}{x}}\\\\b^y = c^z => c = b^{\frac {y}{z}}\\\\b^2 = ac = b^{\frac {y}{x}} * b^{\frac {y}{z}} = b^{\frac {y}{x} + \frac {y}{z}}\\\\Since the base are same, powers must be equal.$

              $2=\frac{y}{x} +\frac{y}{z}\\\\=> 2=y (\frac{1}{x} +\frac{1}{z} ) \\\\=>2=y \frac{(x+z)}{xz} \\\\=>y=\frac{2xz}{x+z}$

Hence Proved .

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