Home
Class 12
MATHS
The minimum value of (x^4+y^4+z^2)/(x y ...

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

A

`sqrt(2)`

B

`2sqrt(2)`

C

`4sqrt(2)`

D

`8sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICS TIPS

    FIITJEE|Exercise ASSERTION - REASONING|8 Videos
  • MATHEMATICS TIPS

    FIITJEE|Exercise MCQ (MULTIPLE CORRECT)|30 Videos
  • MATHEMATICS TIPS

    FIITJEE|Exercise ASSIGNMENT (SECTION (I) : MCQ (SINGLE CORRECT)|120 Videos
  • MATHEMATICS

    FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|15 Videos
  • MATRICES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

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

If x,y,z are positive real numbers show that: sqrt(x^(-1)y)*sqrt(y^(-1)z)*sqrt(z^(-1)x)=1

(sqrt(x)+sqrt(y))^(2)=x+y+2sqrt(xy) and sqrt(x)sqrt(y)=sqrt(xy) , where x and y are positive real numbers . If a=1+sqrt(2)+sqrt(3) and b=1+sqrt(2)-sqrt(3) , then a^(2)+b^(2)-2a-2b=

Find the least positive real number K such that for any positive real numbers x,y,z the following inequality holds x sqrt(y)+y sqrt(z)+z sqrt(x)<=K sqrt((x+y)(y+z)(z+x))

(sqrt(x)+sqrt(y))^(2)=x+y+2sqrt(xy) and sqrt(x)sqrt(y)=sqrt(xy) , where x and y are positive real numbers . If x=2sqrt(5)+sqrt(3) and y=2sqrt(5)-sqrt(3) , then x^(4)+y^(4) =

If x, y, z are distinct positive real numbers is A.P. then (1)/(sqrt(x)+sqrt(y)), (1)/(sqrt(z)+sqrt(x)), (1)/(sqrt(y)+sqrt(z)) are in

factorise 2x^(2)+y^(2)+8z^(2)-2sqrt(2)xy+4sqrt(2)yz-8xz

Assuming that x,y,z are positive real numbers,simplify each of the following: (sqrt(x))^(-(2)/(3))sqrt(y^(4))-:sqrt(xy^(-(1)/(2)))( ii) 243x^(10)y^(5)z^(10)5

FIITJEE-MATHEMATICS TIPS-ASSIGNMENT -OBJECTIVE
  1. The largest, two digit prime factor of ""^(200)C(100) is

    Text Solution

    |

  2. The number of ordered pairs of positive integers (m, n) satisfying m l...

    Text Solution

    |

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

    Text Solution

    |

  4. z is a complex number such that z+1/z=2cos 3^0 ,then the value of z^(2...

    Text Solution

    |

  5. Let the unit vectors vec a, vec b, vec c be the position vectors of t...

    Text Solution

    |

  6. If A=[{:(1,1),(0,1):}] and B=[{:(sqrt(3)//2,1//2),(-1//2,sqrt(3)//2):}...

    Text Solution

    |

  7. The quadratic x^2+a x=b+1=0 has roots which are positive integers, the...

    Text Solution

    |

  8. If the planes x=cy+bz,y=az+cx and z=bx+ay pass through a line then a^(...

    Text Solution

    |

  9. The distance of point of intersection of lines (x-4)/1=(x+3)/-4=(z-1)...

    Text Solution

    |

  10. Let A, B, C be points with position vectors r(1)=2hati-hatj+hatk, r(2)...

    Text Solution

    |

  11. The real numbers x, y satisfy x^(3)-3x^(2)+5x-17=0 and y^(3)-3y^(2)+5y...

    Text Solution

    |

  12. x, y, z in R such that x^(2)+y^(2)+z^(2)=1 and alpha=x^(2)+2y^(2)+3z^(...

    Text Solution

    |

  13. Let A, B, C be three events such that P (exactly one of A or (B) = P (...

    Text Solution

    |

  14. If px^(4)+qx^(3)+rx^(2)+sx+t=|{:(x^(2)+3x,x-1,x+3),(x^(2)+1,2-x,x-3),(...

    Text Solution

    |

  15. In a 4xx4 matrix the sum of each row, column and both the main diagona...

    Text Solution

    |

  16. A unit tengent vector at t = 2 on the curve x=t^(2)+2, y=4t^(3)-5,z=2t...

    Text Solution

    |

  17. If p is a prime and both roots of x^(2)-px-444p=0 are integers, then p...

    Text Solution

    |

  18. If 12 divides the seven digit number ab313ab, then the smallest value ...

    Text Solution

    |

  19. If z is a complex number lying in the fourth quadrant of Argand plane ...

    Text Solution

    |

  20. If vec b is a vector whose initial point divides thejoin of 5 hat ...

    Text Solution

    |