Question 1037781
{{{root(3,x) + sqrt(x) = 1}}}
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{{{root(3,x) - 1 = -sqrt(x)}}}
Square both sides
{{{root(3,x^2) - root(3,8x) + 1 = x}}}
{{{root(3,x^2) = root(3,8x) - 1 + x}}}
Cubing both sides gets messy and results in at least a 6th power of x.
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Using graphical methods,
x =~ 0.18503737524864