Find 1/(a - 1) + 1/(b - 1) where a and b are the roots of the quadratic equation 2x^2-7x+2 = x^2-11x+1.
+2666 \({1 \over (a-1)} + {1 \over (b-1)} = {(b-1) \over (a-1)(b-1)} + {(a-1) \over (a-1)(b-1)} \)
\({(b-1) \over (a-1)(b-1)} + {(a-1) \over (a-1)(b-1)} = {a + b -2 \over {ab−a−b+1}}\)
\({a + b -2 \over {ab−a−b+1}} = {a + b -2 \over {ab−(a+b)+1}}\)
\(2x^2-7x+2 = x^2-11x+1\)
\(x^2 + 4x + 1 = 0\)
\(a + b = -{b \over a} = -4\)
\(ab = {c \over a} = 1\)
\({(-4) - 2 \over (1) - (-4) + 1} = {-6 \over 6} = \color{brown}\boxed{-1}\)
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