# Using functions in Solve [closed]

i wanted to calculate the real roots of a function. To my knowledge the function i defined has no real roots, so i expected an emptyset, but instead i got some Root[...#..] answers by Mathematica.

My first input: i[x_] := (86 - 4*x^2)/4; uaa[x_, y_] := 60 - 9*y^2 - 2*x; Solve[uaa[x, i[x]] == 0, x, Reals]

Then i plugged in the function directly into the Solve and i get the expected anser of emptyset.

Control input: {Solve[60 - 9 (86 - 4*x^2)/4^2 - 2*x == 0, x, Reals]}

How can i change my input in the first input so that i get the emptyset?

Thank you very much

• Sorry for forgetting one line :-( – user34047 Feb 3 '16 at 10:51
• Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Take the tour! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! – Michael E2 Feb 3 '16 at 11:00
• You can format inline code and code blocks by selecting the code and clicking the {} button above the edit window. The edit window help button ? is also useful for learning how to format your questions and answers. You may also find this this meta Q&A helpful – Michael E2 Feb 3 '16 at 11:01
• I get four real solutions from both W|A and Mathematica. Maybe there's a typo? For Root to seem less weird, perhaps see the docs or this Q&A. – Michael E2 Feb 3 '16 at 11:11
• Possible duplicate of (13767) ? – Mr.Wizard Feb 3 '16 at 12:29