Question

Solve:(a+x)^2/3+(a-x)^2/3=3(a^2-x^2)^1/3

Answer 1

arrhhhhgggg!

(a+x)^2/3+(a-x)^2/3=3(a^2-x^2)^1/3
(a+x)^2/3+(a-x)^2/3=3( (a+x)(a-x) )^1/3
divide both sides by (a-x)^(2/3)

(a+x)^(2/3) / (a-x)^(2/3) + 1 =3( (a+x)(a-x) )^1/3 /(a-x)^(2/3)

((a+x)/(a-x))^(2/3) + 1 = 3 (a+x)^(1/3) / (a-x)^(1/3)
((a+x)/(a-x))^(2/3) + 1 = 3 ((a+x)/(a-x))^(1/3)
let ( (a+x)/(a-x) )^(1/3) = y

y^2 + 1 = 3y
y^2 - 3y + 1 = 0
y = (3 ± √5)/2 = 2.618.... or 0.3819...

((a+x)/(a-x))^(1/3) = y
cube both sides
(a+x)/(a-x) = y^3
a+x = ay^3 - x y^3
x + xy^3 = ay^3 - a
x(1 + y^3) = ay^3 - a
x = (ay^3 - a)/(1 + y^3)
you got the value of y, so use your calculator if needed
sub in both values of y

There has to be an easier way, I just can't see it right now.