note that possible values of x are the roots of x^2 + x - 1 = 0 x-x^3 = x(1-x^2) = x^2. taking the square root gives |x| x^2-x^3 = x^2(1-x) = x^4 = (1-x)^2. taking the square root gives x^2 or |1-x| hence the LHS = |x| + x^2 = |x| + |1-x| for x < 0, LHS > 1, which fails
note that possible values of x are the roots of x^2 + x - 1 = 0
x-x^3 = x(1-x^2) = x^2. taking the square root gives |x|
x^2-x^3 = x^2(1-x) = x^4 = (1-x)^2. taking the square root gives x^2 or |1-x|
hence the LHS = |x| + x^2 = |x| + |1-x|
for x < 0, LHS > 1, which fails
(x^2)^(1/2) = |x|, for real x.
Consider the square root of (X-X^3)^(1/2), hence we can get X
4 the second value of x, u r a lier. It's always a pleasure to digest all the details when you perform.