Home
Class 12
MATHS
If the maximum and minimum values of y=(...

If the maximum and minimum values of `y=(x^2-3x+c)/(x^2+3x+c)` are 7 and `1/7` respectively then the value of c is equal to

Text Solution

Verified by Experts

The correct Answer is:
4
`:'y=(x^(2)-3x+c)/(x^(2)+3x+c)`
`impliesx^(2)(y-1)+3x(y+1)+c(y-1)=0`
`:' x epsilon R`
`:.9(y+1)^(2)-4c(y-1)^(2) ge 0`
`(2sqrt(c)y-2sqrt(c))^(2)-(3y+3)^(2)le0`
`implies{(2sqrt(c)+3)y-(2sqrt(c)-3)}{(2sqrt(c)-3)y-(2sqrt(c)+3)}le0`
or `(2sqrt(c)-3)/(2sqrt(c)+3)leyle(2sqrt(c)+3)/(2sqrt(c)-3)`
But given `(2sqrt(c)+3)/(2sqrt(c)-3)=7`
`implies2sqrt(c)+3=14sqrt(c)-21`
or `12sqrt(c)=24` or `sqrt(c)=2`
`:.c=4`
Promotional Banner

Similar Questions

Explore conceptually related problems

The minimum value of y=5x^(2)-2x+1 is

The minimum value of y=5x^(2)-2x+1 is

If x is real , the maximum value of (3x^2+9x+17)/(3x^2+9x+7)"i s"

If x is real, the maximum and minimum values of expression (x^(2)+14x+9)/(x^(2)+2x+3) will be

The maximum & minimum value of y=x+(1)/(x) in interval [(1)/(3),(4)/(3)]

If x^2+y^2=4 then find the maximum value of (x^3+y^3)/(x+y)

Find maximum value of y=2x^(3)-24x+107 in [1, 3].

Let x,y,z in C satisfy |x| = 1, |y-6-8i| = 3 and |z + 1-7i| = 5 respectively, then the minimum value of |x-z| + |y-z| is equal to

If the x= 8+ 3sqrt7 , find the value of x^(2) + (1)/(x^(2)) .