Greece | A Nice Algebra Problem | Math Olympiad | Exponential Equation

[@dhruv7856]

Op

[@SALogics]

You are a genius! ❤

[@nasrullahhusnan2289]

Let u=[4+sqrt(15)]^x
v=[4-sqrt(15)]^x
u+v=62 and uv=1
Thus u(62-u)=1
u²-62u+1=0
u=½[62±sqrt(62²-4)]
=½[62±16sqrt(15)]
=31±8sqrt(15)
=31±2sqrt(16×15)
=[4±sqrt(15)]²
Thus x=2

[@SALogics]

Great! ❤