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

Question

1443 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-08-08T14:57:30

$x = {(1 + \frac{1}{\sqrt{3}})}^{2} = \frac{{(1 + \sqrt{3})}^{2}}{3}$ $color(maroon)(x = (1 + 1/sqrt3)^2 = (1 + sqrt3)^2 / 3$

$\frac{1}{\sqrt{3 x}} + \frac{1}{\sqrt{x}} = 1$ $1/(sqrt(3 x)) + 1 / sqrtx = 1$

$\frac{\sqrt{x} + \sqrt{3 x}}{\sqrt{3 x} \cdot \sqrt{x}} = 1$ $(sqrt x + sqrt(3x) ) / (sqrt (3x) * sqrt x) = 1$

$(\sqrt{3} + 1) \cdot \sqrt{x} = \sqrt{3 x^{2}}$ $(sqrt3 + 1) * sqrt x = sqrt(3x^2)$

$\sqrt{\frac{3 x^{2}}{x}} = \sqrt{3} + 1$ $sqrt((3x^2)/x) = sqrt3 + 1$

$\sqrt{3 x} = \sqrt{3} + 1$ $sqrt(3x) = sqrt3 + 1$

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

$x = {(1 + \frac{1}{\sqrt{3}})}^{2} = \frac{{(1 + \sqrt{3})}^{2}}{3}$ $color(maroon)(x = (1 + 1/sqrt3)^2 = (1 + sqrt3)^2 / 3$