Avoid failure with FindInstance[1 == (c + d Sqrt[3]), {c, d}, Integers]?

Questions
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1

FindInstance[1 == (c + d Sqrt[3]), {c, d}, Integers]

Why does this not return c = 1 and d = 0 in version 5.2?

It says that it can’t find a solution.

2

In[1]:= FindInstance[c + d Sqrt[3.] == 1, {c, d}, Integers]

Out[1]= {{c -> 1, d -> 0}}
3

In version 11.0.1 it does not give any solutions but it does say it can’t solve it, and returns it back unevaluated.

If one changes Sqrt[3] to Sqrt[3.0] then it does return {{c → 1, d → 0}}

4

Thank you. I see now that using the floating point clears it up.