IIT JEE , AIEEE Forum - Mathematics , Algebra

johri_anshuman

If 1 lies between the roots of the equation y²-mx+1 and [x] denotes the greatest integer function then find the value of:

[(4|m|/|x|²+16)^m]

amaron

Hi,anshuman!
I am not sure if i can do this but see:
i assume given expression is =0
implies x= (y^2+1)/m
if m>0
given that 1 lies between the roots implies f(1)*(1/m)<0
(because 1 lies btw. the roots,its sign is opp.to that of the parabola)
as m<0,f(1)should be >0 implies
2/m>0 implies m>0 which is a contradiction.
similarly it does not work for m>0
NOTE:I should'nt be using f(x) as it is not a function but i have used for convenience

johri_anshuman

Experts pls solve this question. I need some help.

sudeep.kumar

Dear anshuman,

1 lies b/w the roots of the given equation...
The roots are -sqrt(mx-1) and +sqrt(mx-1)

Now 1 is always greater than the first root, (as the first root is negative)
So, 1<the second root, solving this, we get,

x < 2/m

Also, the term inside the sqrt shud be +ve (condition for existence of roots of the given eqn) This give

x> 1/m

Hence we get the combined inequality as 1/m < x < 2/m

But now onwards, using this inequality, you will see that for different values of x or m, we get different numerical values of the given expression, and we can say nothing difinite about the greatest integer function of the given expression, unless some othere conditions are given.

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