Let . Then the sum of the elements of is:

Question

Let . Then the sum of the elements of  is:

Canvas Classes · Accepted Answer

🧠 Reduce to a Quadratic in

Read the equation: . The  can be rewritten as , turning the equation into a quadratic in . That is the universal first move whenever you see  alongside  (or  alongside ).

After solving the quadratic, you get one or two values of . For each valid value (in ), list all  that produce it. The question asks for the sum of all such , so list explicitly and add.

A useful symmetry: solutions of  in any interval symmetric about  often come in pairs  that sum to  or similar

More questions from this chapter

More questions from this chapter