Oh, Sorry. one more question; i got the last one:
Find $(1)/(a-1)+(1)/(b-1),$ where $a$ and $b$ are the roots of the quadratic equation $2x^2-7x+2 = 0.$
Thanks! :)
+2666 Note that \({1 \over a - 1} + {1 \over b - 1} = {b-1 \over (a - 1)(b-1)} + {a-1 \over (a - 1)(b-1)} = {a + b - 2 \over ab−a−b+1} = {a + b - 2 \over ab−(a+b)+1} \)
By Vieta's, \(a + b = -{b \over a} = {7 \over 2}\) and \(ab = {c \over a} = {2 \over 2} = 1 \)
Now, just plug these back into the original equation and simplify...
