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by harsh.champ » Wed Feb 17, 2010 6:16 am
The integral solutions of the inequality (5x-1) < (x+1) ^2 < (7x-3) are


A. 2
B. 3
C. 2 , 3
D. 2 , 3 , 4
E. 3 , 4
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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by shashank.ism » Wed Feb 17, 2010 7:07 am
harsh.champ wrote:The integral solutions of the inequality (5x-1) < (x+1) ^2 < (7x-3) are


A. 2
B. 3
C. 2 , 3
D. 2 , 3 , 4
E. 3 , 4
(5x-1) < (x+1) ^2 < (7x-3) -->(5x-1) < ( x ^2+1 +2x) < (7x-3)
--> 3x-2<x ^2<5x-4
3x-2<x ^2 --> x ^2-3x+2>0 -->(x-2)(x-1)>0 --> x<1 or x>2 ------(i)

x ^2<5x-4 --> x ^2-5x+4<0 --> (x-4)(x-1)<0 --> 1<x<4 -------(ii)
from (i) & (ii), we get 2<x<4 so integral [spoiler]soln is 3 Ans . B
[/spoiler]
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by Osirus@VeritasPrep » Wed Feb 17, 2010 7:09 am
shashank.ism wrote:
harsh.champ wrote:The integral solutions of the inequality (5x-1) < (x+1) ^2 < (7x-3) are


A. 2
B. 3
C. 2 , 3
D. 2 , 3 , 4
E. 3 , 4
(5x-1) < (x+1) ^2 < (7x-3) -->(5x-1) < ( x ^2+1 +2x) < (7x-3)
--> 3x-2<x ^2<5x-4
3x-2<x ^2 --> x ^2-3x+2>0 -->(x-2)(x-1)>0 --> x<1 or x>2 ------(i)

x ^2<5x-4 --> x ^2-5x+4<0 --> (x-4)(x-1)<0 --> 1<x<4 -------(ii)
from (i) & (ii), we get 2<x<4 so integral [spoiler]soln is 3 Ans . B
[/spoiler]
So is this the part of the program where you come and post the solutions from complore?
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by shashank.ism » Wed Feb 17, 2010 7:21 am
osirus0830 wrote:
shashank.ism wrote:
harsh.champ wrote:The integral solutions of the inequality (5x-1) < (x+1) ^2 < (7x-3) are


A. 2
B. 3
C. 2 , 3
D. 2 , 3 , 4
E. 3 , 4
(5x-1) < (x+1) ^2 < (7x-3) -->(5x-1) < ( x ^2+1 +2x) < (7x-3)
--> 3x-2<x ^2<5x-4
3x-2<x ^2 --> x ^2-3x+2>0 -->(x-2)(x-1)>0 --> x<1 or x>2 ------(i)

x ^2<5x-4 --> x ^2-5x+4<0 --> (x-4)(x-1)<0 --> 1<x<4 -------(ii)
from (i) & (ii), we get 2<x<4 so integral [spoiler]soln is 3 Ans . B
[/spoiler]
So is this the part of the program where you come and post the solutions from complore?
I have solved the problems myself if in any case u are able to find answer on complore be happy
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by money9111 » Wed Feb 17, 2010 8:23 am
I think the answer is B only! i plugged in the numbers for each one starting with 2... quickly ruled that out in the first step becayse i got 9<9 and thats false... so i eliminated ACD, and then just tried 4 and got 25<25 as the 2nd half... and that's wrong... so B it is...
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by shashank.ism » Wed Feb 17, 2010 8:46 am
money9111 wrote:I think the answer is B only! i plugged in the numbers for each one starting with 2... quickly ruled that out in the first step becayse i got 9<9 and thats false... so i eliminated ACD, and then just tried 4 and got 25<25 as the 2nd half... and that's wrong... so B it is...
ok plugin and elimination is a bit faster method for this problem . Good approach money 1119.
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by harsh.champ » Thu Feb 18, 2010 12:23 am
osirus0830 wrote:
shashank.ism wrote:
harsh.champ wrote:The integral solutions of the inequality (5x-1) < (x+1) ^2 < (7x-3) are


A. 2
B. 3
C. 2 , 3
D. 2 , 3 , 4
E. 3 , 4
(5x-1) < (x+1) ^2 < (7x-3) -->(5x-1) < ( x ^2+1 +2x) < (7x-3)
--> 3x-2<x ^2<5x-4
3x-2<x ^2 --> x ^2-3x+2>0 -->(x-2)(x-1)>0 --> x<1 or x>2 ------(i)

x ^2<5x-4 --> x ^2-5x+4<0 --> (x-4)(x-1)<0 --> 1<x<4 -------(ii)
from (i) & (ii), we get 2<x<4 so integral [spoiler]soln is 3 Ans . B
[/spoiler]
So is this the part of the program where you come and post the solutions from complore?
Hey osirus,
This is a very common type of math question and can be found in various sources.I don't know whether it is there in complore also.

As for the soln. approach ,we can find that the plugging technique is better suited for the question and it can be solved easily.


Another approach is plotting the lines y=5x-1 and y=7x-3 and the quadratic curve:(x+1)^2 and then solving it through the graph.
[This method is only for those people who are very well conversant with the graphical approach.In case ,you are not,don't use this method on the exam.It can backfire also if you don't have adequate practice of graphical approach]
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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