Home
Class 11
MATHS
Given that x ,y ,z are positive real suc...

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.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

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

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

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^2+y^2+z^2= xy+yz+zx then find the value of (x+y):z.

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=2 , that the maximum value of z=(4)/(x)+(36)/(y) is less than its minimum value .

If y z+z x+x y=12 , and x , y , z are positive values, find the greatest value of x y zdot

If x,y,z, in R such that x+y+z=4, x^2+y^2+z^2=6 then find the range of x.

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

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. For anyx ,y , in R^+,x y >0 . Then the minimum value of (2x)/(y^3)+(x...

    Text Solution

    |

  2. If a ,b ,a n dc are positive and 9a+3b+c=90 , then the maximum value o...

    Text Solution

    |

  3. Given that x ,y ,z are positive real such that x y z=32. If the minimu...

    Text Solution

    |

  4. If the product of n positive numbers is n^n , then their sum is (a)...

    Text Solution

    |

  5. If a,b,c are different positive real numbers such that b+c−a,c+a−b and...

    Text Solution

    |

  6. Find the greatest value of x^2 y^3, where x and y lie in the first qua...

    Text Solution

    |

  7. Find the maximum value of (7−x)^4 (2+x)^5 when x lies between −2 and ...

    Text Solution

    |

  8. If a1, a2,...... ,an >0, then prove that (a1)/(a2)+(a2)/(a3)+(a3)/(a4...

    Text Solution

    |

  9. If a > b and n is a positive integer, then prove that a^n-b^n > n(a b)...

    Text Solution

    |

  10. If a ,b ,a n dc are positive and a+b+c=6, show that (a+1//b)^2+(b+1/...

    Text Solution

    |

  11. Prove that [(x^2+y^2+z^2)/(x+y+z)]^(x+y+z)> x^x y^y z^z >[(x+y+z)/3]^(...

    Text Solution

    |

  12. Prove that 1^1xx2^2xx3^3xxxxn^nlt=[(2n+1)/3]^(n(n+1)/2),n in Ndot

    Text Solution

    |

  13. Prove that 2/(b+c)+2/(c+a)+2/(a+b)lt1/a+1/b+1/c ,where a ,b ,c>0.

    Text Solution

    |

  14. The minimum value of 2^(sin x) + 2^(cos x) is

    Text Solution

    |

  15. In how many parts an integer N>=5 should be divide so that the produc...

    Text Solution

    |

  16. In triangle ABC internal angle bisector AI,BI and CI are produced to m...

    Text Solution

    |

  17. The minimum value of (x^4+y^4+z^2)/(x y z) for positive real numbers x...

    Text Solution

    |

  18. If x ,y ,z are positive real number, then show that sqrt((x^(-1)y)xsqr...

    Text Solution

    |

  19. The least value of 6tan^2varphi+54cot^2varphi+18 is (I)54 when A.M.g...

    Text Solution

    |

  20. A rod of fixed length k slides along the coordinates axes, If it meet...

    Text Solution

    |