Home
Class 12
MATHS
If a+b+c=1 and a>0,b>0,c>0 then prove th...

If `a+b+c=1` and `a>0,b>0,c>0` then prove that `ab^2c^3le1/(432)`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • Product of two Vectors

    A DAS GUPTA|Exercise Exercise|48 Videos

  • Properties and Application of definite Integrals

    A DAS GUPTA|Exercise EXERCISE|62 Videos

Similar Questions

Explore conceptually related problems

If a+2b+3c=1 and a>0,b>0,c>0 and the greatest value of a^(3)b^(2)c is (1)/(k) then (k-5180) is

If a>0,b>0,c>0 prove that a/(b+c)+b/(c+a)+c/(a+b)ge3/2 .

If the points (a,0),(b,0),(0,c), and (0,d) are concyclic (a,b,c,d>0), then prove that ab=cd.

If a+b+c=0, then prove that ((b+c)^(2))/(3bc)+((c+a)^(2))/(3ac)+((a+b)^(2))/(3ab)=1

If 2a+b+3c=1 and a gt 0, b gt 0, c gt 0 , then the greatest value of a^(4)b^(2)c^(2)"_____" .

If a+b+3c=1 and a gt 0, b gt 0, c gt 0 , then the greratest value of a^(2)b^(2)c^(2) is

If (1)/(a)+(1)/(a-b)+(1)/(c)+(1)/(c-b)=0 and a+c-b!=0, then prove that a,b,c are in H.P.

If a,b,c are all non zero and a+b+c=0 , prove that (a^2)/(bc)+(b^2)/(ca)+(c^2)/(ab)=3 .

If a+b+c=0, an^(2)+bn+c=0 and a+bn+cn^(2)=0 where n!=0, 1 , then prove that a=b=c=0

A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
  1. If a+2b+3c=1 and a>0 , b>0 , c>0 and the greatest value of a^3b^2c is...

    Text Solution

    |

  2. If 4a+3b+2c=5 and a>0,b>0,c>0 then the greatest value of a^2b^3c^4 wil...

    Text Solution

    |

  3. If a+b+c=1 and a>0,b>0,c>0 then prove that ab^2c^3le1/(432).

    Text Solution

    |

  4. Find the greatest value of the product of three positive numbers if th...

    Text Solution

    |

  5. Find the sum of n terms of the series 1*2*3+2*3*4+3*4*5...........

    Text Solution

    |

  6. Sum to n terms :1*3^2+3*5^2+5*7^2+...

    Text Solution

    |

  7. Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+,...

    Text Solution

    |

  8. Sum the series : (1*2)+(1*2+2*3)+(1*2+2*3+3*4)+... to 12 brackets.

    Text Solution

    |

  9. If a1,a2,a3,...,an be in AP whose common difference is d then prove th...

    Text Solution

    |

  10. Find the sum of n terms of the series 1 *2 *3 + 2*4*6 + 3*6*9+...

    Text Solution

    |

  11. Find the sum of n terms of the series 1 + 9 +24 + 46 + 75................

    Text Solution

    |

  12. Find the nth term and sum to n tems of the following series: 3+6+11+18...

    Text Solution

    |

  13. If tn=sum1^n n, find Sn=sum1^n tn.

    Text Solution

    |

  14. Find the sum of n terms of the series 1^2 + 4^2+ 7^2 + .........

    Text Solution

    |

  15. Find the sum of the series 2 + 5 + 14 +41 + 122 +.... up to n terms an...

    Text Solution

    |

  16. The sum to n terms of series 1+(1/2+1/(2^2))+1+(1/2+1/(2^2)+1/(2^3)+1/...

    Text Solution

    |

  17. Find the sum to n terms of the series 5+ 11 + 19 + 29+ 41+ ……

    Text Solution

    |

  18. The sum of first 9 terms of the series (1^(3))/(1)+(1^(3)+2^(3))/(1+3)...

    Text Solution

    |

  19. Find the sum to n terms of the series 1^(2)/(1)+(1^(2)+2^(2))/(1+2)...

    Text Solution

    |

  20. Find sum n^3 from n=1 to n=100.

    Text Solution

    |