Home
Class 9
MATHS
Prove the following where a,b,x m,ngt0 ...

Prove the following where `a,b,x m,ngt0`
`(a^3+b^3)/(a^2+b^2)gt(a^2+b^2)/(a+b)gt(a+b)/2(aneb)`.

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

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

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

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

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

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

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

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

Prove that (a^2+b^2)/2gt((a+b)/2)(aneb) .

Prove that 1/(a+b)+1/(a-b)gt1/sqrt(a^2-b^2)(agtb) .

Prove the following (cos ^2A* sin^2 B)- (sin^2 A* cos ^2B)= cos^2 A- cos ^2B

KALYANI PUBLICATION-INEQUALITIES AND INEQUATIONS-EXERCISE
  1. Prove the following where a,b,x m,ngt0 (m^3+n^3)/(m^2+n^2)ge(m^2+n^2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Prove that 1/(a+b)+1/(a-b)gt1/sqrt(a^2-b^2)(agtb).

    Text Solution

    |

  5. Prove that (a^2+b^2)/2gt((a+b)/2)(aneb).

    Text Solution

    |

  6. Prove that (a+b)^2gt14(a+b)-49(agt0,bgt0).

    Text Solution

    |

  7. Find the value of x for which the following expressions aquire greates...

    Text Solution

    |

  8. Find the value of x for which the following expressions acquire greate...

    Text Solution

    |

  9. Find the value of x for which the following expression...

    Text Solution

    |

  10. Find the value of x for which the following expression...

    Text Solution

    |

  11. Find the greatest value of x in order that. 7x^2+11gex^3+17x.

    Text Solution

    |

  12. Find the least value of x in order that. 3x^3+7xge8x^2+2.

    Text Solution

    |

  13. (b^3+c^3)/(b+c)+(c^3+a^3)/(c+a)+(a^3+b^3)/(a+b)gtab+bc+ca

    Text Solution

    |

  14. If a,b,c are positive unequal real numbers then prove that 1/a+1/b+1...

    Text Solution

    |

  15. If a,b,c are positive unequal real numbers then prove that (bc)/a+(c...

    Text Solution

    |

  16. If a,b,c are positive unequal real numbers then prove that b^2c^2+c^...

    Text Solution

    |

  17. If a,b,c are positive unequal real numbers then prove that (a+b+c)(1...

    Text Solution

    |

  18. If a,b,c,e,f,g are positive unequal real numbers then prove that (a/...

    Text Solution

    |

  19. If a,b,c are positive unequal real numbers then prove that a^2+b^2+c...

    Text Solution

    |

  20. prove that sqrt7+sqrt12gtsqrt6+sqrt13.

    Text Solution

    |