How do you solve $\frac{x}{2} = \sqrt{3 x}$ $x/2=sqrt(3x)$ ?

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Answer 1 · 2015-08-19T12:50:33

The solutions are
$x = 0$ $color(blue)(x=0$

$x = 12$ $color(blue)(x=12$

$\frac{x}{2} = \sqrt{3 x}$ $x/2=sqrt(3x)$

Squaring both sides
${(\frac{x}{2})}^{2} = {(\sqrt{3 x})}^{2}$ $(x/2)^2=(sqrt(3x))^2$

$\frac{x^{2}}{4} = 3 x$ $x^2/4=3x$

$x^{2} = 3 x \cdot 4$ $x^2=3x*4$

$x^{2} = 12 x$ $x^2=12x$

$x^{2} - 12 x = 0$ $x^2-12x=0$

Factorising the expression:

$x (x - 12) = 0$ $x(x-12)=0$

Solution 1:
$x = 0$ $color(blue)(x=0$

Solution 2
$x - 12 = 0$ $x-12=0$
$x = 12$ $color(blue)(x=12$

How do you solve x/2=sqrt(3x)x2=√3xx/2=sqrt(3x)?