Home
Class 12
MATHS
Given that x,y,z are positive real numbe...

Given that `x,y,z` are positive real numbers such that `xyz=32`, the minimum value of `sqrt((x+2y)^(2)+2z^(2)-15)` is equal to

A

`6`

B

`8`

C

`9`

D

`12`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `(x^(2)+2xy+2xy+4y^(2)+z^(2)+z^(2))/(6) ge (16x^(4)y^(4)z^(4))^(1//6)`
`(x+2y)^(2)+2z^(2) ge 96`
`(x+2y)^(2)+2z^(2)-15 ge 81`
`:.` Least value of `sqrt((x+2y)^(2)+2z^(2)-15)` is `9`
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Comprehension|2 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Examples|37 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|222 Videos

Similar Questions

Explore conceptually related problems

Given that x,y,z are positive reals such that xyz=32 . The minimum value of x^2+4xy+4y^2+2z^2 is ___________.

Given that x ,y ,z are positive real such that x y z=32. If the minimum value of x^2+4x y+4y^2+2z^2 is equal m , then the value of m//16 is.

If x,y,z are positive real numbers such that x^(2)+y^(2)+Z^(2)=7 and xy+yz+xz=4 then the minimum value of xy is

If x ,y ,a n dz are positive real umbers and x=(12-y z)/(y+z) . The maximum value of x y z equals.

If x and y are positive real numbers such that 2log(2y - 3x) = log x + log y," then find the value of " x/y .

The x , y , z are positive real numbers such that (log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3, then the value of (1/(2z)) is ............

If x,y,z be three positive numbers such that xyz^(2) has the greatest value (1)/(64) , then the value of (1)/(x)+(1)/(y)+(1)/(z) is

The minimum value of (x^4+y^4+z^2)/(x y z) for positive real numbers x ,y ,z is (a) sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) 8sqrt(2)

If ( x +y+z ) = 9 and ( xy + yz + zx ) = 26 then find the value of x^(2) + y^(2) z^(2)