SOLUTION: 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

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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
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
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
Suppose x+y = xy

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

x = a%2Fb and y = c%2Fd

Then 

a%2Fb%22%22%2B%22%22c%2Fd%22%22=%22%22a%2Fb×c%2Fd

a%2Fb%22%22%2B%22%22c%2Fd%22%22=%22%22%28ac%29%2F%28bd%29

Multiply every term through by bd

 ad + bc = ac

-ac + ad = -bc

 ac - ad = bc

a(c - d) = bc

a = %28bc%29%2F%28c-d%29, c≠d

Choose any three numbers b, c and d, such that c≠d

Choose a = %28bc%29%2F%28c-d%29

Then x = a%2Fb and y = c%2Fd

will be such that x+y = xy

Example:

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

Let a = %28bc%29%2F%28c-d%29 = %283%2A7%29%2F%287-2%29 = 21%2F5 = 4.2

Then x = a%2Fb = 4.2%2F3 = 1.4

And y = c%2Fd = 7%2F2 = 3.5 

Then x+y = 1.4 + 3.5 = 4.9

And xy = 1.4×3.5 = 4.9

Edwin