An inspired problem

Algebra Level 3

$\frac{ 72^x + 81^x }{54^x + 108^x } = \frac{72 + 81 }{ 54 + 108 }$

Find the number of values of $x$ which satisfies the above equation.

1 5 0 4 2

1 solution

Faisal Basha
Mar 29, 2015

x = 1, -1 the LHS = RHS

Your solution simply shows that $1,(-1)$ are two solutions to the equation. It doesn't show that there are no more solutions for $x$ .

Here's a brief proof of the claim that there are no more solutions for $x$ other than $(\pm 1)$ . First, note that $72\times 81=54\times 108$ . Using the proof posted here , our claim is proved.

Prasun Biswas - 6 years, 1 month ago

An inspired problem

1 solution

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