Question 767962
find all possible numbers whose sum and product are same. example 2+ 2=4 & 2*2=4, 1.5*3 = 4.5 & 1.5 + 3 = 4.5
<pre>
Suppose x+y = xy

Suppose a,b,c, and d are numbers such that

x = {{{a/b}}} and y = {{{c/d}}}

Then 

{{{a/b}}}{{{""+""}}}{{{c/d}}}{{{""=""}}}{{{a/b}}}×{{{c/d}}}

{{{a/b}}}{{{""+""}}}{{{c/d}}}{{{""=""}}}{{{(ac)/(bd)}}}

Multiply every term through by bd

 ad + bc = ac

-ac + ad = -bc

 ac - ad = bc

a(c - d) = bc

a = {{{(bc)/(c-d)}}}, c&#8800;d

Choose any three numbers b, c and d, such that c&#8800;d

Choose a = {{{(bc)/(c-d)}}}

Then x = {{{a/b}}} and y = {{{c/d}}}

will be such that x+y = xy

Example:

Choose b=3, c=7, d=2

Let a = {{{(bc)/(c-d)}}} = {{{(3*7)/(7-2)}}} = {{{21/5}}} = 4.2

Then x = {{{a/b}}} = {{{4.2/3}}} = 1.4

And y = {{{c/d}}} = {{{7/2}}} = 3.5 

Then x+y = 1.4 + 3.5 = 4.9

And xy = 1.4×3.5 = 4.9

Edwin</pre>