What is the difference between the minimum and the maximum values of [x / (x^2 + 8x + 24)] given that x is real?
1. [square root (6)] / 2
2. [square root (6)] / 4
3. [square root (6)] / 8
4. square root (6)
For more questions related to Quant visit:
http://www.thesmartant.club/forum/44/quantitative-...
http://www.thesmartant.club/forum/11/quant-doubts/
http://www.thesmartant.club/forum/14/quantitative-...
Top Scorers till day 2: http://www.thesmartant.club/forum/thread/489/top-s...
Last update on October 13, 5:30 am by Rahil Choudhary.
Let x/(x^2+8x+24)=m
Solvong this equation by cross multiplying we get
mx^2+(8m-1)x+24m=0
Because it is real
Discrimant>=0
(8m-1)^2-4(24m^2)>=0
=> -32m^2-16m+1>=0
Therefore m has roots as (-2-root(6))/8,(-2+root(6))/8
Which are the min and max values
Therefore difference is
Root(6)/4
Answer is 2
Suppose the given expression is taken as y on cross multiplication and making it a quadratic in x we get the following equation
yx^2 + x(8y – 1) + 24y = 0
In order to ensure that 'x' is a real number, discriminant to be greater than or equal to zero.
(8y-1)^2 -4y*(24y) >=0
32y^2 +16y -1 <=0
roots turn out as ({-16 +- root(384)}/64}
so maximum value is (-2 -root(6))/8 and maximum value is (-2+root(6))/8 so their reuired difference is root(6)/4
HEnce option b
Last update on October 13, 6:00 am by Parmeshwar.
B sqrt(6)/4
Using differentiation rule,
Max and minima occur at x= +/- sqrt(24)
Hence diff is B
Then according to u amswer is root(6)*4 not root(6)/4
Then according to u amswer is root(6)*4 not root(6)/4
d/dx= {(x^2+8x+24)-x(2x+8)}/(x^2+8x+24)^2=0 at Maxima and Minima
x^2=24 ie x=+/- sqrt24
at x=+sqrt24 we get value of function as 1/ {4sqrt6+8} Minima
at x=-sqrt24 we get value of function as -1/ {4sqrt6-8}Maxima
Difference is sqrt6/4
No where it is mentioned in the rules stated by you that a picture cannot be uploaded. Neither ur interface is nice enough....kindly remove the option of attaching files and others. Totally unfair
No where it is mentioned in the rules stated by you that a picture cannot be uploaded. Neither ur interface is nice enough....kindly remove the option of attaching files and others. Totally unfair
Dear Parmeshwar,
We understand your concern, but allowing an image explanation would be unfair for others who type their answers. Simran raised the same concern with us over mail prior to the question going Live, and was denied to do so. There are still 400 points to be won, we are sure that with your competitive skills and abundance knowledge you would be a tougher competition for others.
Thank you for the feedback, we are working on the interface to make it more user friendly.
Also, congratulations on winning 100 points on this question.
Regards,
The Smart Ant Club
Last update on October 13, 11:49 am by Rahil Choudhary.
d/dx= {(x^2+8x+24)-x(2x+8)}/(x^2+8x+24)^2=0 at Maxima and Minima
x^2=24 ie x=+/- sqrt24
at x=+sqrt24 we get value of function as 1/ {4sqrt6+8} Minima
at x=-sqrt24 we get value of function as -1/ {4sqrt6-8}Maxima
Difference is sqrt6/4
Dear Moinuddin,
This is the explanation that we require to be eligible for the contest. The comment before this wouldn't be considered.
Congratulations on winning 50 points.
Regards,
The Smart Ant Club
Consider, [x/(x^2 + 8x + 24)] = m
x = mx^2 + 8mx + 24m
mx^2 + x(8m – 1) + 24m = 0
To ensure that x is a real number, we must have discriminant of this quadratic equation greater than or equal to 0.
(8m-1)^2 – 4m(24m) >= 0
64m^2 -16m + 1 – 96m^2 >= 0
-32m^2 – 16m + 1 >= 0
32m^2 + 16m + 1 <=0
The root of the equation 32m^2 + 16m 1 = 0 are
1. [-16 +- (square root(384)] / 64
2. [-2 +- (square root(6)] / 8
Hence,
the minimum value of the expression is [-2 – square root(6)] / 8
the maximum value of the expression is [-2 + square root(6)] / 8
Required Difference is ([-2 + square root(6)] / 8) – ([-2 – square root(6)] / 8) = square root(6) / 4. Ans 2