Radical Equation | Can You Beat This Algebra Challenge?

[@RashmiRay-c1y]

Let x+2=u and 3-x=v. Then u^3/2+v^3/2 = 9 and u+v=5. Let u^1/2+v^1/2 = a and u^1/2v^1/2=b. Then, a^2=5+2b and a^3=9+3ab > b=1/2(a^2-5) > a^3-15a+18=0. a=3 is a valid solution > b=2. Thus, u^1/2 + 2/u^1/2=3 > u^1/2=1,2 > u=1,2 > x = -1,2.

[@潘博宇-k4l]

X=-1, 2.

[@Quest3669]

X= 2; -1

[@kassuskassus6263]

x=-1 and x=2

[@RealQinnMalloryu4]

(x^3+8)+ (27 ➖ x^3)=8x^3+{x^0+ x^0 ➖ }={8x^3+x^1}=8x^4 2^3x^2^2 1^1^2x^1^1 2x^1 (x ➖ 2x+1).