Home
Class 12
MATHS
Find the greatest value of x^2y^3z^4 if ...

Find the greatest value of `x^2y^3z^4` if `x^2+y^2+z^2=1,w h e r ex ,y ,z` are positive.

Text Solution

Verified by Experts

We have
`(2(x^2)/(2)+3(y^2)/(3)+4(z^2)/(4))/(9) ge(((x^2)/(2))^2((y^2)/(3))^3((z^2)/(4))^4)^((1)/(9))`
`rArr (1)/(9^9) ge(x^4y^6x^8)/(2^23^34^4)`
`rArr x^4y^6z^8 le (2^23^34^4)/(9^9) `
`rArr x^2y^3z^4 le 2^5xx3^(-(15)/(2))`
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

Find the greatest value of x^(2)y^(3)z^(4) if x^(2)+y^(2)+z^(2)=1, where x,y,z are positive.

The value of |[yz, z x,x y],[ p,2p,3r],[1, 1, 1]|,w h e r ex ,y ,z are respectively, pth, (2q) th, and (3r) th terms of an H.P. is a.-1 b. 0 c. 1 d. none of these

If x,y,z are positive intergers and x+y+z=240 and x^2 + y^2= z^2 then find the number of positive solutions.

Find the coffiecient of x^2 y^3 z^4 w in the expansion of (x-y-z+w)^(10)

Find the number of integral solutions of x+y+z+y 2,y>1,z>=2,w>=0

Find the value of x,y, and z if : (i) [[3,x4,y]]=2.[[-1.5,1z,1]]

Find the value of (( x -y )^3 + ( y - z )^3 + ( z - x )^3 )/ (9 ( x - y )( y - z ) ( z - x )) 1 . 0 2 . 1/9 3 . 1/3 4. 1