Ques:- When x is real what is the least value of (x**2-6*x+5)/(x**2+2*x+1)
Recent Answer : Added by Admin On 2020-05-17 12:01:23:
(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
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Recent Answer : Added by Biplab On 2021-07-31 16:35:59:
76
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Recent Answer : Added by Admin On 2020-05-17 12:01:12:
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Recent Answer : Added by Admin On 2020-05-17 12:01:22:
37
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Recent Answer : Added by Admin On 2020-05-17 12:00:33:
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Recent Answer : Added by Manik rattan On 2021-08-16 06:56:14:
suppose
pipe:
A -30 hours A’s effeciency (60/30) =2
60( lcm of 30 and 20)
B- 20 hours B’s effeciency (60/20)=3
time taken by both to fill = 60/5 =12 as given in question (effeciencies of both a+b =2+3=5)
time taken by faster pipe i.e b = 60/3 =20
Ques:- Product of three consecutive nos. 210. What is the sum of two least numbers?
Recent Answer : Added by Admin On 2020-05-17 12:02:28:
5 * 6 * 7 = 210 ,
Two Least No’s are 5,6
There fore 5+6=11 is answer
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Recent Answer : Added by Admin On 2020-05-17 12:03:55:
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A. 3700
B. 2960
C. 740
D. 680
Recent Answer : Added by R.Geethanjali On 2022-04-02 06:59:22:
FLRIHO=cooler