South Korea l Nice Olympiad Math Exponential Problem l find x=?

[@korlanaganandasai6233]

Very good solution.

[@The_Esemor]

Good

[@ChavoMysterio]

x²⁷+x¹⁸=36
(x⁹)³+(x⁹)²-36=0
Let y=x⁹
y³+y²-36=0
y³-27+y²-9=0
(y-3)(y²+3y+9)+(y-3)(y+3)=0
(y-3)(y²+4y+12)=0
y²+4y+12=0
y²+4y+4=-8
(y+2)²=-8
|y+2|=2i_/2
y+2=±2i_/2
y=-2±2i_/2
x⁹=-2±2i_/2
x=⁹_/(-2±2i_/2) ❤❤
y-3=0
y=3
x⁹=3
x=⁹_/3 ❤
24 more roots