Home
Class 11
MATHS
If a+b+c=1, then prove that 8/(27a b c)>...

If `a+b+c=1,` then prove that `8/(27a b c)>{1/a-1}{1/b-1}{1/c-1}> 8.`

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

Prove that (a^8+b^8+c^8)/(a^3b^3c^3)>1/a+1/b+1/c

If a ,b , a n dc are distinct positive real numbers such that a+b+c=1, then prove that ((1+a)(1+b)(1+c))/((1-a)(1-b)(1-c))> 8.

If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+1//(1//a c),c+1//(a b) are also in A.P.

If in a triangle A B C ,/_C=60^0, then prove that 1/(a+c)+1/(b+c)=3/(a+b+c) .

If in a triangle A B C ,/_C=60^0, then prove that 1/(a+c)+1/(b+c)=3/(a+b+c) .

If b is the harmonic mean between a and c, then prove that (1)/(b - a) + (1)/(b - c) = (1)/(a) + (1)/(c)

If a ,b ,c are in A.P., prove that 1/(b c),1/(c a),1/(a b), is also in A.P.

If a b c=1,\ show that 1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1

If a b c=1, show that 1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1

If a >0,b >0 and c >0 prove that (1984, 2M) (a+b+c)(1/a+1/b+1/c)geq9

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If (log)(10)(x^3+y^3)-(log)(10)(x^2+y^2-x y)lt=2, and x ,y are positiv...

    Text Solution

    |

  2. If (log)2(a+b)+(log)2(c+d)geq4. Then find the minimum value of the exp...

    Text Solution

    |

  3. If a+b+c=1, then prove that 8/(27a b c)>{1/a-1}{1/b-1}{1/c-1}> 8.

    Text Solution

    |

  4. If a ,b , a n dc are distinct positive real numbers such that a+b+c=1,...

    Text Solution

    |

  5. Prove that b^2c^2+c^2a^2+a^2b^2> a b cxx(a+b+c)(a ,b ,c >0) .

    Text Solution

    |

  6. Find the minimum value of 4sin^(2)x+4cos^(2)x .

    Text Solution

    |

  7. Prove that (a b+x y)(a x+b y)>4a b x y(a , b ,x ,y >0)dot

    Text Solution

    |

  8. The minimum value of the sum of real number a^-5,a^-4,3a^-3,1,a^8 and ...

    Text Solution

    |

  9. If a1,a2,------ ,an are positive real numbers whose product is a fixe...

    Text Solution

    |

  10. If a ,b ,c ,d are positive real umbers such that a+b+c+d=2,then M=(a+...

    Text Solution

    |

  11. A straight line through the vertex P of a triangle P Q R intersects th...

    Text Solution

    |

  12. If alpha in (0,pi/2), then sqrt(x^2+x)+tan^2alpha/sqrt(x^2+x) is alw...

    Text Solution

    |

  13. In A B C , prove that cos e c A/2+cos e c B/2+cos e c C/2geq6.

    Text Solution

    |

  14. In Delta A B C , prove that t a n A+t a n B+t a n Cgeq3sqrt(3),w h e...

    Text Solution

    |

  15. If a ,b ,c are real numbers such that 0 < a < 1,0 < b < 1,0 < c < 1,a+...

    Text Solution

    |

  16. If a^2+b^2+c^2=x^2+y^2+z^2=1, then show that a x+b y+c z leq1.

    Text Solution

    |

  17. Prove that a^4+b^4+c^4> a b c(a+b+c),w h e r ea ,b ,c > 0.

    Text Solution

    |

  18. Prove that the greatest value of x y is c^3/sqrt(2a b), if a^2x^4+b^2y...

    Text Solution

    |

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

    Text Solution

    |

  20. If y = sin^-1(10x) + pi/2 then find the value of dy/dx .

    Text Solution

    |