sanju09 wrote:Value of the expression (x^2 - x + 1)/ (x - 1) cannot lie between
(A) -1, -3
(B) 1, -3
(C) -1, 2
(D) -1, 3
(E) 1, 3

Nice idea, sanju09!

I will give my shot, ok?

Answer: D

Let the expression given be equal to m, where m is a fixed real number. It is easy to come to the following 2o degree equation in the (real) variable x:

x^2 - x(1+m)+(1+m) = 0

Calculating the discriminant and imposing it NEGATIVE, we will get m^2 - 2m - 3 < 0, then we have -1 < m < 3.

Interpretation: for values of m between -1 and 3, there are no real numbers x such that the expression is equal to m.

That´s what you had in mind?

Best Regards,
Fábio.

sanju09 wrote:Value of the expression (x^2 - x + 1)/ (x - 1) cannot lie between
(A) -1, -3
(B) 1, -3
(C) -1, 2
(D) -1, 3
(E) 1, 3


[spoiler]Made up[/spoiler]

IMO D.

Just tried some value by taking x=0,1,-1,-1/2

fskilnik wrote:

sanju09 wrote:Value of the expression (x^2 - x + 1)/ (x - 1) cannot lie between
(A) -1, -3
(B) 1, -3
(C) -1, 2
(D) -1, 3
(E) 1, 3

Nice idea, sanju09!

I will give my shot, ok?

Answer: D

Let the expression given be equal to m, where m is a fixed real number. It is easy to come to the following 2o degree equation in the (real) variable x:

x^2 - x(1+m)+(1+m) = 0

Calculating the discriminant and imposing it NEGATIVE, we will get m^2 - 2m - 3 < 0, then we have -1 < m < 3.

Interpretation: for values of m between -1 and 3, there are no real numbers x such that the expression is equal to m.

That´s what you had in mind?

Best Regards,
Fábio.

hmmm...so you read minds too!! Well, you certainly deserve an on records 'THANKS' from me. Nice job, sir

Thanks!