Home
Class 11
MATHS
For anyx ,y , in R^+,x y >0 . Then the ...

For any`x ,y , in R^+,x y >0` . Then the minimum value of `(2x)/(y^3)+(x^3y)/3+(4y^2)/(9x^4)` is.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos
  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If x^2+y^2=4 then find the maximum value of (x^3+y^3)/(x+y)

If x^2+y x^2=4 then find the xamimum value of (x^3+y^3)/(x+y)

If x ,y in R and x^2+y^2+x y=1, then find the minimum value of x^3y+x y^3+4.

Evaluate : (i) (2x + 3y) ( 3x +4y)

If x=4 and y=1, find the value of ((x)/(2)-(y)/(3))((x^(2))/(4)+(xy)/(6)+(y^(2))/(9)) .

If 3x+2y=12 and x y=6 , find the value of 9x^2+4y^2

Evaluate : (v) (3x - 4y) (3x + 4y) (9x^ + 16y^2)

If 2x+3y=8 and x y=2 , find the value of 4x^2+9y^2

If (4x )/(2y)=4, what is the value of (3y)/(x) ?

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. True / False For every intger n >1 , the inequality (n !)^(1//n)<(n+1)...

    Text Solution

    |

  2. If x ,y in R^+ satisfying x+y=3, then the maximum value of x^2y is.

    Text Solution

    |

  3. For anyx ,y , in R^+,x y >0 . Then the minimum value of (2x)/(y^3)+(x...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. The minimum value of 2^sinx+2^cosx

    Text Solution

    |

  17. In how many parts an integer N>=5 should be dissected so that the pro...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If x+y+z=1a n dx ,y ,z are positive, then show that (x+1/x)^2+(y+1/y)^...

    Text Solution

    |