If x₁, x₃ are the roots of ax² – 6x + 1 = 0 and x₂, x₄ are the roots of 21x²–bx+1 = 0; x₁, x₂, x₃, x₄ are in H.P. then (a, b) =

The given equations are ax² – 6x + 1 = 0.....(i), 

and 21x²–bx+1 = 0....(ii)

the roots of eq.(i) are  x₁, x₃

the roots of eq.(ii) are x₂, x₄

_{and given that} x₁, x₂, x₃, x₄ are in H.P.

$\begin{array}{l}\frac{1}{{\mathrm{x}}_1}-\frac{1}{{\mathrm{x}}_3}=\frac{1}{{\mathrm{x}}_2}-\frac{1}{{\mathrm{x}}_4}\Rightarrow \sqrt{36-4\mathrm{a}}=\sqrt{{\mathrm{b}}^2-84}\\ \Rightarrow {\mathrm{b}}^2=120-4\mathrm{a}\end{array}$