When x is real what is the least value of
(x**2-6*x+5)/(x**2+2*x+1)
- 4 Answers
- 9105 Views
- Geometric Software, GSSL, I also Faced
- E-Mail Answers
Answer Posted / kermit rose
(x**2 - 6* x + 5) = (x-1)*(x-5)
(x**2 + 2 * x + 1) = (x + 1) * (x+1) = (x+1)**2
For what x is (x-1)*(x-5)/( (x+1)**2) a minimum?
One way to answer this question is by using calculus.
Take the derivative, and set to zero.
Since this is a fraction of polynomials, and a fraction is
zero only if it's numerator is zero, we need calculate only
the numerator of the derivative and set it to zero.
The numerator of the
Derivative of (x-1)*(x-5)/( (x+1)**2) is
( (x-1) + (x-5) ) ( x+1)**2 - (x-1)(x-5)( 2 (x+1) )
= (2 x - 6) (x+1)**2 - (2) (x-1)(x-5) (x+1)
= 0
Divide through by 2 (x+1)
(x-3)(x+1) - (x-1)(x-5) = 0
(x**2 - 2 x - 3 ) - (x**2 - 6 x + 5) = 0
x**2 - x**2 - 2 x + 6 x - 3 - 5 = 0
4 x - 8 = 0
x = 2
Plugging in x = 2 into the original
(x**2-6*x+5)/(x**2+2*x+1)
gives us (2**2 - 6 * 2 + 5)/(2**2 + 2*2 + 1)
= (4 - 12 + 5) / (4 + 4 + 1) = -3/9 = -1/3
Least value is -1/3
| Is This Answer Correct ? | 1 Yes | 0 No |
Post New Answer View All Answers
A clock with the hours round the face in Roman block numbers, as illustrated in the sketch fell down and the dial broke into four parts....
An article sold at a profit of 20% if both the c.p & s.p were to be Rs.20/- the profit would be 10% more. What is the c.p of that article?
Given 10 alphabets out of which 5 are to be chosen. How many words can be made with atleast one repetition.
he hour hand lies between 3 and 4. Tthe difference between hour and minute hand is 50 degree.What are the two possible timings?
what is the exact qualifing marks for group 1 prelims
Two candles of equal lengths and diff thickness are there. The thicker one last 6 hrs ,the thinner 2 hrs less than thicker .Ramesh lit the two candle at same time , when he went to bed he saw that thicker one is twice the length of thinner one. For how long Ramesh lit the candles.
halley is clarks father& arthur is halleys father.after some years when halleys age is equal to arthurs age,halleys age becomes 5 times of clarks present age.clarks age then is 8 times his fathers present age. sum of arthur & halleys age is 100 find clarks present age
Find the least value of 3x + 4y if x2y3 = 6.
if a man reduces the selling price of a fan from 400 to 380 his loss increases by 20% .cost price of fan is.
Four Members A, B, C, D are playing a game .A person losing a game should double the amount of others .B, C, D are losing in order after three games .The amount after 3 games are A&B having 40,D is having 16&C 80.What amount did B have?
hai frnds pls give me some tips and traps about HP software company interview for freshers.am a B.E CSE fresher.hoe will be the interview?how many days it will be conducted?how will be apps round?technical round?hr round?pls help me if any one known means.send me that pattern by vijay ,chennai
if x=y=2z and xyz =256 then x=
Find the missing word(...),ayw,gec,mki,sqo
In a group of 15,7 have studied Latin, 8 have studied Greek, and 3 have not studied either.How many of these studied both Latin and Greek
i need icet solved papers 2000 to 20010,and also mock papers,mock online
