exponential equation(3): to Shubhodip.

\textbf{Solve The equation}:\\\\ \mathbf{\sqrt{4^x-6^x+9^x}+\sqrt{9^x-3^x+1}+\sqrt{4^x-2^x+1}=2^x+3^x+1}

2 Answers

\sqrt{a^2+b^2-ab}+\sqrt{b^2+1-b}+\sqrt{a^2+1-a}=a+b+1

Try to prove that \sqrt{a^2+b^2-ab}\ge \frac{a+b}{2}

Hence it is easy to prove that a=b=1

so x=0

Missed it.:)

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