Find 1/(a - 1) + 1/(b - 1), where a and b are the roots of the quadratic equation 2x^2 - 9x + 2 = 0.
+128408 By Vieta
The sum of the roots = a + b = 9/2
The product of the roots = ab = 2/2 = 1
And note that
1/ ( a - 1) + 1 /( b - 1) =
b -1 + a - 1
_____________ =
(a - 1) ( b - 1)
a + b - 2
____________ =
ab - a - b + 1
( a + b) - 2
_______________ =
ab - (a + b) + 1
9/2 - 2
__________ =
1 - (9/2) + 1
5/2
_______ =
-5/2
-1
