Home
Class 9
MATHS
For xgt1 and ygt1 prove that (x+1)(y+1)l...

For `xgt1` and `ygt1` prove that `(x+1)(y+1)lt2(xy+1)`.

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES AND INEQUATIONS

    KALYANI PUBLICATION|Exercise EXERCISE|126 Videos

  • HARDER PRODUCT AND FACTORISATION

    KALYANI PUBLICATION|Exercise EXERCISE|148 Videos

  • LOGARITHMS

    KALYANI PUBLICATION|Exercise EXERCISE|122 Videos

Similar Questions

Explore conceptually related problems

If a,b, c and x, y, z are all positive and unequal, then prove that, (xy+1)(yz+1)(zx+1)gt8xyz[sqrtxy+1/(sqrtxy)gt2 etc]

If x, y, z are all positive real numbers, then prove that, If x+y+z=1 , then prove that (1-x)(1-y)(1-z)ge8xyz .

Prove that 1/4ltlog_10 2lt1/3

Prove that 1/3ltlog_10 3lt1/2

If xy^2=1 , then prove that 2(dy)/(dx)+y^3=0

If tan^-1 x+tan^-1 y+tan^-1 z=pi , prove that x+y+z=xyz

Prove that 3/10ltlog_10 2lt1/3

If tan^-1 x+tan^-1 y+tan^-1 z=pi/2 , prove that xy+yz+zx=1

Solve (1-x^(2))(dy)/(dx)-xy=1

KALYANI PUBLICATION-INEQUALITIES AND INEQUATIONS-EXERCISE
  1. For xgt1 and ygt1 prove that (x+1)(y+1)lt2(xy+1).

    Text Solution

    |

  2. State whether the following statements are true or false. If false giv...

    Text Solution

    |

  3. State whether the following statements are true or false. If false giv...

    Text Solution

    |

  4. State whether the following statements are true or false. If false giv...

    Text Solution

    |

  5. State whether the following statements are true or false. If false giv...

    Text Solution

    |

  6. State whether the following statements are true or false. If false giv...

    Text Solution

    |

  7. State whether the following statements are true or false. If false giv...

    Text Solution

    |

  8. State whether the following statements are true or false. If false giv...

    Text Solution

    |

  9. State whether the following statements are true or false. If false giv...

    Text Solution

    |

  10. State whether the following statements are true or false. If false giv...

    Text Solution

    |

  11. State whether the following statements are true or false. If false giv...

    Text Solution

    |

  12. Compare the pairs of real number given below a^3+1,a^2+1.

    Text Solution

    |

  13. Compare the pairs of real number given below a^3+b^3,a^2b+ab^2.

    Text Solution

    |

  14. Compare the pairs of real number given below ab+1,a+b.

    Text Solution

    |

  15. Prove the following where a,b,x m,ngt0 m^5+n^5gem^4n-mn^4.

    Text Solution

    |

  16. Prove the following where a,b,x m,ngt0 a^6+b^6gea^5b+ab^5.

    Text Solution

    |

  17. Prove the following where a,b,x m,ngt0 a^(m+n)+b^(m+n)gea^mb^n+a^nb^...

    Text Solution

    |

  18. Prove the following where m,ngt0 m^3-n^3gt(m-n)^3, (mgtn).

    Text Solution

    |

  19. Prove the following where a,b,m,ngt0 (m+2n)/(m+3n)ge(m+n)/(m+2n).

    Text Solution

    |

  20. Prove the following where a,b,x m,ngt0 (m^3+n^3)/(m^2+n^2)ge(m^2+n^2...

    Text Solution

    |

  21. Prove the following where a,b,x m,ngt0 (a-c)/bge(b-c)/a+(a-b)/b(0lta...

    Text Solution

    |