Find the exact solution for

(√(5) - 1)/(x) = (√(5))/(2)

Then, find the approximate solution.

Question

Find the exact solution for

(√(5) - 1)/(x) = (√(5))/(2)

Then, find the approximate solution.

anonymous · Answer

$$\frac{ \sqrt{5} - 1 }{ x } =\frac{ \sqrt{5} }{ 2 }$$

anonymous · Answer

reciprocal will also be equal to each other:
$$\frac{x}{\sqrt5-1}=\frac{2}{\sqrt5}$$

at this point multiply both sides by (sqrt5 -1)

anonymous · Answer

To be honest I don't know anything about this. Only very little about square roots...

anonymous · Answer

since it asks for an 'exact solution, you can keep the squareroots as they are.  just have to get x by itself

anonymous · Answer

By multiplying /5 -1 on each side?  How do I go about that?

anonymous · Answer

$$\cancel{(\sqrt5-1)}\times\frac{x}{\cancel{\sqrt5-1}}=\frac{2}{\sqrt5}\times (\sqrt5-1)$$

anonymous · Answer

it's exactly like it sounds.  by multiplying each side by the same quantity you preserve the equal sign, then one side simplifies.

it can also be considered a move across the equal sign, and above the division sign

anonymous · Answer

So from $$x = \frac{ 2 }{ \sqrt{5} } x (\sqrt{5} - 1)$$ I just multiply that side and get the answer?

anonymous · Answer

Well one of the answers.