Home
Class 12
MATHS
If G and L are the greatest and least va...

If G and L are the greatest and least values of the expression`(2x^(2)-3x+2)/(2x^(2)+3x+2), x epsilonR` respectively.
The least value of `G^(100)+L^(100)` is

A

`2^(100)`

B

`3^(100)`

C

`7^(100)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Let `y=(2x^(2)-3x+2)/(2x^(2)+3x+2)`
`implies2x^(2)y+3xy+2y=2x^(2)-3x+2`
`implies2(y-1)x^(2)+3(y+1)x+2(y-1)=0`
As `x epsilonR`
`:.Dge0`
`=9(y+1)^(2)-4.2(y-1).2(y-1)ge0`
`implies9(y+1)^(2)-16(y-1)^(2)ge0`
`implies(3y+3)^(2)-(4y-4)^(2)ge0`
`implies(7y-1)(7-y)ge0`
`implies(7y-1)(y-7)le0`
`:.1/7leyle7`
`:.G=7` and `L=1/7`
`:.GL=1`
NOw `(G^(100)+L^(100))/2ge(GL)^(100)implies(G^(100)+L^(100))/2ge1`
`impliesG^(100)+L^(100)ge2`
Least value of `G^(100)` +L^(100)` is 2.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|2 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise The Straight Lines Exercise 8 : (Questions Asked in Previous 13 years Exams)|1 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Three Dimensional Coordinate System Exercise 12 : Question Asked in Previous Years Exam|2 Videos

Similar Questions

Explore conceptually related problems

If G and L are the greatest and least values of the expression (x^(2)-x+1)/(x^(2)+x+1), x epsilon R respectively. then find the least value of G^(5)+L^(5) .

If G and L are the greatest and least values of the expression (2x^(2)-3x+2)/(2x^(2)+3x+2), x epsilonR respectively. If L^(2)ltlamdaltG^(2), lamda epsilon N the sum of all values of lamda is

If G and L are the greatest and least values of the expression (2x^(2)-3x+2)/(2x^(2)+3x+2), x \in R resectively. G and L are the roots of the equation

If G and L are the greatest and least values of the expression (x^(2)-x+1)/(x^(2)+x+1), x epsilon R respectively then G and L are the roots of the equation

If G and L are the greatest and least values of the expression (x^(2)-x+1)/(x^(2)+x+1), x epsilon R respectively then If L lt lamdalt G and lamda epsilon N , the sum of all values of lamda is

If x= -1 then value of expression x^(2)-2x+3 is 2.

Find the least value of the expression x^(2) + 4y^(2) + 3z^(2) - 2x - 12y -6z + 14

Least value of the function , f(x)=2^(x^2)-1+2/(2^(x^2)+1) is :

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

The least values of cosec^(2) x + 25 sec^(2)x is

Home
Profile