Let α > 1 be irrational. Several authors studied the numbers l~m(α) = inf{|y| : y ∈ Λ_m, y ≠ 0}, where m is a positive integer and Λ_m denotes the set of all real numbers of the form y = ε_0α~n + ε_1α~(n-1) + … + ε_(n-1)α + ε_n with restricted integer coefficients |ε_i| ≤ m. The value of l~1(α) was determined for many particular Pisot numbers and l~m(α) for the golden number. In this paper the value of l~m(α) is determined for irrational numbers α, satisfying α~2 = αα ± 1 with a positive integer a.
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