Question

Given \[(x+y)/x=x/y\]

what is \(x(y)\)

Answer 1

\[\varphi \]

Answer 2

show working

Answer 3

x/y = 1+y/x

Answer 4

Let's say that \(LHS = \varphi\)\[\varphi = 1 + \dfrac{1}{\varphi}\]Leaves you with a quadratic.

Answer 5

(Here, I meant \(\varphi\) a variable.)

Answer 6

I meant the RHS.

Answer 7

Well, same thing. :)

Answer 8

\(\sf{
a = 1 + \cfrac{1}{a} \\
a^2 - a - 1 = 0 \\
a = \cfrac{1 \pm \sqrt{1 + 4}}{2} \\
a = \cfrac{1 \pm \sqrt{5}}{2} \\}\)

Where : \(\boxed{\color{blue}{\space a = \cfrac{x}{y} }}\)

Answer 9

Represent pair of perpendicular lines passing through origin. Wow!