Home
Class 12
MATHS
If a and b are positive numbers such tha...

If a and b are positive numbers such that `a^(2) + b^(2) = 4`, then find the maximum value of `a^(2) b`.

Text Solution

Verified by Experts

The correct Answer is:
`(16)/(3sqrt(3))`
Using `A.M ge G.M`., we get
`((a^2)/(2)+(a^3)/(2)+b^2)/(3g)ge((a^2)/(2)(a^2)/(2)b^2)^((1)/(3))`
`rArr (4)/(3) ge ((a^2b)^((2)/(3)))/(2^((2)/(3)))`
`rArr (a^2b) le ((4)/(3))^((3)/(2))xx 2=(16)/(3sqrt(3))`
Therefore , maximum value of `a^2b is (16)/(3sqrt(3))`.
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Exercise 6.4|4 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Exercise (Single)|20 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Exercise 6.2|6 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|324 Videos

Similar Questions

Explore conceptually related problems

If a and b are positive integers such that a^(2)-b^(4)=2009, find a+b

If a and b are positive real numbers such that a^(2)b^(3)=(4)/(9), then least value of a+b is

If a,b,c are positive real numbers such that a +b+c=18, find the maximum value of a^(2)b^(3)c^(4)

If a, b, c and d are four positive numbers such that a+b+c+d=4 , then what is the maximum value of (a+1)(b+1)(c+1)(d+1) ?

If a and b are two positive real numbers such that 4a^2 + b^2 = 20 and ab = 4, then the value of 2a+b is : यदि a और b दो सकारात्मक वास्तविक संख्याए है जैसे कि 4a^2 + b^2 = 20 और ab = 4, तो 2a+b का मान:

If a,b,c, are positive numbers such that 2a+3b+4c=9, then

If a,b and c are real number such that a^(2)+b^(2)+2c^(2)=4a-2c+2bc-5, then find the possible value of the total number of (6a-4b-2c)

Let a,b and c be real numbers such that a+2b+c=4. Find the maximum value of (ab+bc+ca)