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

`sqrt2`

B

`2sqrt2`

C

`4sqrt2`

D

`8sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    DISHA PUBLICATION|Exercise EXERCISE -1 : Concept Builder|60 Videos

  • RELATIONS AND FUNCTIONS-2

    DISHA PUBLICATION|Exercise EXERCISE-2: CONCEPT APPLICATOR|30 Videos

  • SETS

    DISHA PUBLICATION|Exercise EXERCISE-2 : CONCEPT APPLICATOR|30 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

DISHA PUBLICATION-SEQUENCES AND SERIES -Exercise -2 : Concept Applicator
  1. If 1,log9(3^(1-x)+2), log3(4*3^x-1) are in A.P then x equals to

    Text Solution

    |

  2. In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binom...

    Text Solution

    |

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

    Text Solution

    |

  4. If every even term of a series is a times the term before it and every...

    Text Solution

    |

  5. If y=3^(x-1)+3^(-x-1) (where, x is real), then the leastvalue of y is

    Text Solution

    |

  6. Let a1, a2, a3, ...an be an AP. Prove that: 1 / (a1 an) + 1 / (a2 a(n-...

    Text Solution

    |

  7. Concentric circles of radii 1,2,3,. . . . ,100 c m are drawn. The inte...

    Text Solution

    |

  8. If log(e)5, log(e)(5^(x) -1) and log(e)(5^(x)-(11)/(5)) are in A.P the...

    Text Solution

    |

  9. If a ,b ,c are the sides of a triangle, then the minimum value of a/(b...

    Text Solution

    |

  10. The value of 1/(2!) +2/(3!) +...+999/(1000!) is equal to

    Text Solution

    |

  11. If a,b,c are in H.P.then which one of the following is true

    Text Solution

    |

  12. If a,b,c and the d are in H.P then find the vlaue of (a^(-2)-d^(-2))/(...

    Text Solution

    |

  13. The odd value of n for which 704 + 1/2 (704) + 1/4 (704) + ... upto n ...

    Text Solution

    |

  14. If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6p!=1 , then the value o...

    Text Solution

    |

  15. The harmonic mean of (a)/(1 - ab) and (a)/(1 + ab) is :

    Text Solution

    |

  16. The sum of the infinite series(2^(2))/(2!) + (2^(4))/(4!) + (2^(6))/(6...

    Text Solution

    |

  17. If a,b,c re in H.Pthen which one of the following is true

    Text Solution

    |

  18. ABC is a right angled triangle in which /B=90^(@) and BC=a. If n point...

    Text Solution

    |

  19. If S(1), S(2), S(3),...,S(n) are the sums of infinite geometric series...

    Text Solution

    |

  20. If a is the A.M. of ba n dc and the two geometric mean are G1a n dG2, ...

    Text Solution

    |