United States | A HARD Math Olympiad Problem!

[@Math_Mysteries_Unlocked]

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[@saragilani-j1q]

Very interesting.

[@Math_Mysteries_Unlocked]

Thanks!

[@LloydCash-he1qv]

8ˣ + 4ˣ = 150
Let y = 2ˣ
y³ + y² - 150 = 0
(y - 5)(y² + 6y + 30) = 0
y = 5 or y² + 6y + 30 = 0
y = -3 ± i.√21
Therefore
y = 5 or y = -3 ± i.√21
2ˣ = 5 2ˣ = √30e^(i.(π ± arctan(√21/3)))
x = log₂5 xln(2) = ln(30)/2 + i.(π ± arctan(√21/3))
x = ln(30)/(2ln(2)) + i.(π ± arctan(√21/3))/ln(2)

[@Math_Mysteries_Unlocked]

Brilliant! Thank you for your comment!