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minimum possible value

by Gurpinder » Wed Sep 01, 2010 9:44 am
if x ≥ 4 + (z+1)^2, what is the minimum possible value for x?


I am not sure if my technique is right but i tend to get a quadratic eq. on the right side.

x ≥ 4+ (z+1)(z+1)
x ≥ 4+z^2+2z+1
x ≥ z^2+2z+5

and i get stuck here......
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by this_time_i_will » Wed Sep 01, 2010 9:53 am
sud be 4, put z=-1
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by Gurpinder » Wed Sep 01, 2010 9:55 am
this_time_i_will wrote:sud be 4, put z=-1
why z=-1?
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by diebeatsthegmat » Wed Sep 01, 2010 2:42 pm
Gurpinder wrote:if x ≥ 4 + (z+1)^2, what is the minimum possible value for x?


I am not sure if my technique is right but i tend to get a quadratic eq. on the right side.

x ≥ 4+ (z+1)(z+1)
x ≥ 4+z^2+2z+1
x ≥ z^2+2z+5

and i get stuck here......
i think( for what i remember when i was in high school)
to x minimum (z+1)^2+4 must be minimumor (z+1)^2<-4
is the answer -4?
i am not sure much
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by puneetdua » Thu Sep 02, 2010 12:16 am
Hi Gurpinder,

I think 'this_time_i_wrote' is correct -
We need to find the minimum possible value of x So - it is coming out to be 4 when we put z = -1

if we put z = 0 - > x >= 5
z= 1 - > x >= 8

z = -2 -> x>=5

Z = -1 --> x >=4

4 is the minimu possible value from above inputs ....
If this is really wrong ...please reply back..
Thanks
Puneet
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by Gurpinder » Thu Sep 02, 2010 6:04 am
puneetdua wrote:Hi Gurpinder,

I think 'this_time_i_wrote' is correct -
We need to find the minimum possible value of x So - it is coming out to be 4 when we put z = -1

if we put z = 0 - > x >= 5
z= 1 - > x >= 8

z = -2 -> x>=5

Z = -1 --> x >=4

4 is the minimu possible value from above inputs ....
If this is really wrong ...please reply back..
Thanks Puneet.

You are right. He is correct and so are you. The logic behind this question was to get the minimum possible value first for the term that's being squared. The least value we can get for that term is 0 if x = -1. And therefore x>=4.
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by dinesh19aug » Thu Sep 02, 2010 6:42 am
For any questions which asks what should be the maximum or minimum value, always look for the constant terms first.

In this question, it says x>= 4 + (Z+1)^2.

For X to be minimum, the unknown variable should be minimum.
What is the unknown here??? ======> (Z+1).
Now Can Z+1 be negative ???? ....... Sure if Z was negative .... BUT it is squared.
So what do we know from this??? ====> (Z+1)^2 can never be negative.
So waht can be minimum possible value??? ====> 0. And when can this be 0?? ===> When Z = -1.

So X will be minimum when term (Z+1)^2 is minimum.

So Minimum value = 4 Answer.

I hope this helps.
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