Wolfram|Alpha displays only one integer root out of infinity

Questions
, ,
1

(a+b)=2(c+d), 2ab=cd

noname.jpg
noname.jpg1187×932 129 KB

a=1,b=45,c=5,d=18 satisfies this equation, but Wolfram doesn’t display it

2

Wolfram|Alpha does not say “this is the only possible integer solution”, and you did not ask for all solutions. Mathematica can find more:

In[121]:= FindInstance[
 a + b == 2 (c + d) && 2 a b == c d && a == 1 && b > 0, {a, b, c, 
  d}, Integers, 4]

Out[121]= {{a -> 1, b -> 33, c -> 6, d -> 11}, {a -> 1, b -> 33, 
  c -> 11, d -> 6}, {a -> 1, b -> 45, c -> 5, d -> 18}, {a -> 1, 
  b -> 45, c -> 18, d -> 5}}
3

Thank you for the reply!
Have a nice day.