Home
Class 11
MATHS
Prove that ((bc+ac+ab)/(a+b+c))^(a+b+c)g...

Prove that `((bc+ac+ab)/(a+b+c))^(a+b+c)ge(b)^a(c)^b(a)^c` [where `a,b,c gt 0]`.

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

if a:b = b:c prove that ((a+b)/(b+c))^2 = (a^2+b^2)/(b^2+c^2) .

Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)(c- a)

If a : b = c : d , then prove that (a +b)/(a - b) = sqrt(ac + ad + bc + bd)/sqrt(ac - ad - bc + bd) .

If a,b,c,d be four consecutive coefficients in the binomial expansion of (1+x)^(n) , then value of the expression (((b)/(b+c))^(2)-(ac)/((a+b)(c+d))) (where x gt 0 and n in N ) is

If a/b = b/c = c/d , then prove that (a^(2) + b^(2) + c^(2))(b^(2) + c^(2)+d^(2)) = (ab + bc cd)^(2)

Prove that, abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)) =4 a^2b^2c^2 .

Prove that 2/(b+c)+2/(c+a)+2/(a+b)lt1/a+1/b+1/c ,where a ,b ,c>0.

Three numbers a,b,c are such that (a^(2) +ab+b ^(2))/(ab +bc +ca) =(a+b)/(a+c), then the numbers b, a, c are in-

If a, b, c are in A.P., show that, (bc)/(a(b+c)), (ca)/(b(c+a)) and (ab)/(c(a+b)) are in H.P.

Without expanding the determinant, prove that {:|( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) |:} ={:|( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) |:}

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Show that a^2(1+b^2)+b^2(1+c^2)+c^2(1+a^2)ge6abc.

    Text Solution

    |

  2. If m, n are positive quantities, prove that ((mn+1)/(m+1))^(m+1)gen^m.

    Text Solution

    |

  3. Prove that ((bc+ac+ab)/(a+b+c))^(a+b+c)ge(b)^a(c)^b(a)^c [where a,b,c ...

    Text Solution

    |

  4. If log2,log(2^n-1) and log(2^n+3) are in A.P. then n =

    Text Solution

    |

  5. If the ratiio of the sum of n terms ofd two AP's is (3n+1):(2n+3) then...

    Text Solution

    |

  6. If a1,a2,a3,.......an are in AP where a1 gt 0foralli then the value of...

    Text Solution

    |

  7. Given p no. of A.P. each of which consists of an n terms. If their fir...

    Text Solution

    |

  8. Answer the following question based on above passage: The coefficient...

    Text Solution

    |

  9. If a,b,c ,d and p are distinct real number such that (a^2+b^2+c^2)p^2-...

    Text Solution

    |

  10. Suppose a,b,c are in A.P and a^2,b^2,c^2 are in G.P. If a lt b lt c an...

    Text Solution

    |

  11. The value of 4^(1/3).4^(1/9).4^(1/27)....infty is.

    Text Solution

    |

  12. If the sum of an infinite GP is 20 and sum of their square is 100 then...

    Text Solution

    |

  13. If S=1+a+a^2+....... t o infty , then a=

    Text Solution

    |

  14. If 4a^2+9b^2+16c^2=2(3ab+6bc+4ca) where a,b,c are non zero real number...

    Text Solution

    |

  15. If a,b,c in AP and x=sum(n=0)^inftya^n,y=sum(n-0)^inftyb^n,z=sum(n-0)^...

    Text Solution

    |

  16. If a,b,c are in G.P., then the equations ax^2+2bx+c =0 and dx^2+2ex+f ...

    Text Solution

    |

  17. If the product of n positive number is unity, then their sum is

    Text Solution

    |

  18. If x1gt0,i=1,2.....50 and x1+x2+.....x50=50 then the minimum value of ...

    Text Solution

    |

  19. If a,b,c,d are positive real number such that a+b+c+d=2 , then M=(a+b)...

    Text Solution

    |

  20. If a1,a2,.....an are positive real number whose product is a fixed num...

    Text Solution

    |