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Question

Let r, s, and t be the roots of the equation x^3 - 20x^2 + 18x - 7 = 0. Find the value of (1+r)(1+s)(1+t).

Accepted Answer

Expanding, we have (1+r)(1+s)(1+t) = 1 + (r+s+t) + (rs+st+tr) + rst.By Vieta's formulas, this comes out to 1 + 20 + 18 + 7 = 46.