1/root^3x + 1/rootx =1 x=?

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Answer 1 · 2018-08-08T14:57:30

$color(maroon)(x = (1 + 1/sqrt3)^2 = (1 + sqrt3)^2 / 3$

$1/(sqrt(3 x)) + 1 / sqrtx = 1$

$(sqrt x + sqrt(3x) ) / (sqrt (3x) * sqrt x) = 1$

$(sqrt3 + 1) * sqrt x = sqrt(3x^2)$

$sqrt((3x^2)/x) = sqrt3 + 1$

$sqrt(3x) = sqrt3 + 1$

sqrtx = (sqrt 3 + 1) / sqrt 3#

$color(maroon)(x = (1 + 1/sqrt3)^2 = (1 + sqrt3)^2 / 3$