Algebra Level 4

Let the harmonic mean of two positive real numbers $$a$$ and $$b$$ be 4. If $$q$$ is a positive real number such that $$a, \ 5, \ q, \ b$$ is an arithmetic progression, then find the value(s) of $$|q-a|$$. $\begin{array}{} (1) \, 1 \quad \quad \quad \quad \quad \quad \quad \quad & (2) \, 2 \\ (3) \, 3 & (4) \, 5 \end{array}$ Note:

• Submit your answer as the increasing order of the serial numbers of all the correct options.

• For eg, if your answer is $$(1),(2)$$, then submit 12 as the correct answer, if your answer is $$(2),(3),(4)$$, then submit 234 as the correct answer.

×