quadratic

eqn is x² - (a + 1)x + (a - 1) = 0

D = a² + 2a + 1 - 4 (a - 1) = a² - 2a + 5 = (a - 1)² + 4 > 0 for all a E R

thus, this eqn. will hv real and distinct roots for all a E R

Now, using ur method,
a (x - 1) = x² - x - 1

or, a = x² - x - 1x - 1 = x + 1 - xx - 1

Now, since, x is an integer then the only values of x for xx - 1 to be an integer are 0 and 2

setting x = 0 and 2 we get, a = 1 and 1

Thus, the only value of a is 1

nt sure used ur way... 'nakal mein bhi akal chahiye' :P