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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10, SAT-II.

What is a possible value of k be for:

equation

to be the reciprocal of:

equation

If the two numbers are to be reciprocals then they must multiply to 1:

equation

equation

Apply the sum and difference identity:

equation

and solve for k:

equation

equation

equation

Only the negative root is among the answer choices.