i tried to times everything by 4x to take away the surd but i got nowhere.

solve the following equation

x-8 = 2√x

2. Originally Posted by Miasmagasma
i tried to times everything by 4x to take away the surd but i got nowhere.

solve the following equation

x-8 = 2√x
$\displaystyle x-8 = 2\sqrt{x}$

square both sides ...

$\displaystyle x^2 - 16x + 64 = 4x$

$\displaystyle x^2 - 20x + 64 = 0$

$\displaystyle (x - 4)(x-16) = 0$

now ... which solution works in the original equation?

3. Originally Posted by Miasmagasma
i tried to times everything by 4x to take away the surd but i got nowhere.

solve the following equation

x-8 = 2√x
$\displaystyle x - 8 = 2\sqrt{x}$

$\displaystyle (x - 8)^2 = (2\sqrt{x})^2$

$\displaystyle x^2 - 16x + 64 = 4x$

$\displaystyle x^2 - 20x + 64 = 0$

$\displaystyle (x - 16)(x - 4) = 0$

$\displaystyle x = 4$ or $\displaystyle x = 16$.

Darn, beaten...

4. thanks guys, i made the stupid error of squaring the 8 initially, rather than the whole side.

5. ... please note that only one of the two solutions is valid.