Hello 200001 Originally Posted by
200001 (1+x)/x = sqrt3
I am struggling to get the hang of this. i have multiplied both sides by x and ended up with 1+ x = xsqrt3
Any help please?
You're right so far. Now solve this as you would any other equation: get the $\displaystyle x$'s on one side and everything else on the other.$\displaystyle 1+x = x\sqrt3$
$\displaystyle \Rightarrow 1 = x\sqrt3 -x$
Factorise:$\displaystyle \Rightarrow 1 = x(\sqrt3-1)$
Divide:$\displaystyle \Rightarrow x = \frac{1}{\sqrt3 -1}$
You can leave the answer like this, but it's neater if you 'rationalise the denominator':
$\displaystyle \Rightarrow x = \frac{1}{\sqrt3 -1}\color{red}\times \frac{\sqrt3+1}{\sqrt3+1}$
$\displaystyle = \frac{\sqrt3+1}{3-1}$
$\displaystyle =\frac{\sqrt3+1}{2}$
Grandad