Home
Class 11
MATHS
If x and y are positive real numbers an...

If `x and y` are positive real numbers and `m, n` are any positive integers, then prove that `(x^n y^m)/((1+x^(2n))(1+y^(2m))) lt 1/4`

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,y are positive real numbers and m, n are positive integers, then prove that (x^(n) y^(m))/((1 + x^(2n))(1 + y^(2m))) le (1)/(4)

Let x, y be positive real numbers and m, n be positive integers, The maximum value of the expression (x^(m)y^(n))/((1+x^(2m))(1+y^(2n))) is

If n is a positive integer, prove that |I m(z^n)|lt=n|I m(z)||z|^(n-1.)

If m and n are positive quantites , prove that ((mn+1)/(m+1))^(m+1)ge n^(m)

For any positive real number a and for any n in N , the greatest value of (a^(n))/(1+a+a^(2)+…+a^(2n)) , is

If and n are positive integers, then lim_(x->0)((cosx)^(1/ m)-(cosx)^(1/ n))/(x^2) equal to :

If a ,\ m ,\ n are positive integers, then {root(m)root (n)a}^(m n) is equal to (a) a^(m n) (b) a (c) a^(m/n) (d) 1

For any positive real number x , prove that there exists an irrational number y such that 0 lt y lt x .

If x cos A + y sin A = m and x sin A - y cos A = n, then prove that : x^(2) + y^(2) = m^(2) + n^(2)

Prove that if xa n dy are odd positive integers, then x^2+y^2 is even but not divisible by 4.

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If a+b=1,a >0, prove that (a+1/a)^2+(b+1/b)^2geq(25)/2dot

    Text Solution

    |

  2. If Cr=(n !)/([r !(n-r)]), the prove that sqrt(C1)+sqrt(C2)+.......sq...

    Text Solution

    |

  3. If x and y are positive real numbers and m, n are any positive integ...

    Text Solution

    |

  4. The least value of the expression 2(log)(10)x-(log)x(0. 01),forx >1, i...

    Text Solution

    |

  5. If a , b , c , are positive real numbers, then prove that (2004, 4M) {...

    Text Solution

    |

  6. True / False For every intger n >1 , the inequality (n !)^(1//n)<(n+1)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |