Home
Class 11
MATHS
If a ,b , a n dc are distinct positive r...

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.`

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 a, b, c are positive real numbers such that a + b + c = 1 , then prove that a/(b + c)+b/(c+a) + c/(a+b) >= 3/2

If a,b,c and d are four positive real numbers such that abcd=1 , what is the minimum value of (1+a)(1+b)(1+c)(1+d) .

If a, b, c are positive real numbers such that a+b+c=1 , then the greatest value of (1-a)(1-b)(1-c), is

If a, b, c are distinct positive real numbers such that a+(1)/(b)=4,b+(1)/( c )=1,c+(1)/(d)=4 and d+(1)/(a)=1 , then

If a ,b ,c are real numbers such that 0 < a < 1,0 < b < 1,0 < c < 1,a+b+c=2, then prove that a/(1-a)b/(1-b)c/(1-c)geq8

If a, b, c are three distinct positive real numbers, then the least value of ((1+a+a^(2))(1+b+b^(2))(1+c+c^(2)))/(abc) , is

If a , b , c , are positive real numbers, then prove that (2004, 4M) {(1+a)(1+b)(1+c)}^7>7^7a^4b^4c^4

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

If a+b+c=1 and a, b, c are positive real numbers such that (1-a)(1-b)(1-c)gelambda" abc, then "lambda =

If a, b, c are positive real numbers, then the least value of (a+b+c)((1)/(a)+(1)/(b)+(1)/( c )) , is

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If (log)2(a+b)+(log)2(c+d)geq4. Then find the minimum value of the exp...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. 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

    |

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

    Text Solution

    |

  15. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If a+b=1,a >0, prove that (a+1/a)^2+(b+1/b)^2geq(25)/2dot

    Text Solution

    |