若抛物线y=x的平方-(k-1)x-3k-2与x交于点A(a,0),B(b,0)且a的平方+b的平方=17,则k=______.

△ = (k - 1)^2 + 4(3k + 2) = k^2 + 10k + 9 >= 0, k=-1 a+b = k - 1,ab = -3k-2 由a^2 + b^2 = 17,有(a+b)^2 - 2ab = 17 (k-1)^2 + 2(3k + 2) = 17,得k = -6(舍去)或k = 2 所以k = 2