Home
Class 11
MATHS
If three positive real numbers a,b ,c ar...

If three positive real numbers `a,b ,c` are in A.P such that `a b c=4` , then the minimum value of `b` is a)`2^(1//3)` b) `2^(2//3)` c) `2^(1//2)` d) `2^(3//23)`

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

If a,b,c are positive real numbers such that a + b +c=18, find the maximum value of a^2b^3c^4

If three positive numbers a, b, c are in A.P. and 1/a^2,1/b^2,1/c^2 also in A.P. then

If a,b,c are positive real numbers and 2a+b+3c=1 , then the maximum value of a^(4)b^(2)c^(2) is equal to

Ifa, b, c are positive real number such that ab^(2)c^(3) = 64 then minimum value of ((1)/(a) + (2)/(b) + (3)/(c)) is equal to

If a , b , c are real numbers forming an A.P. and 3+a , 2+b , 3+c are in G.P. , then minimum value of ac is

If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the minimum value of a+b+c is (a) 1 (b) 3 (c) 5 (d) 9

If a, b, c are positive real number such that lamba abc is the minimum value of a(b^(2)+c^(2))+b(c^(2)+a^(2))+c(a^(2)+b^(2)) , then lambda =

If a ,b ,c ,d are distinct integers in an A.P. such that d=a^2+b^2+c^2, then find the value of a+b+c+d

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 are three distinct positive real numbers in G.P., then prove that c^2+2a b >3ac

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. Statement 1: If the arithmetic mean of two numbers is 5/2 geometric ...

    Text Solution

    |

  2. Let the positive numbers a ,b ,ca d nd be in the A.P. Then a b c ,a b ...

    Text Solution

    |

  3. If three positive real numbers a,b ,c are in A.P such that a b c=4 , t...

    Text Solution

    |

  4. Consider an infinite geometric series with first term a and common rat...

    Text Solution

    |

  5. The maximum sum of the series 20+19 1/3+18 2/3+...... is (A) 310 (...

    Text Solution

    |

  6. In the quadratic equation ax^2+bx+c=0,Delta = b^2-4ac and alpha+beta,a...

    Text Solution

    |

  7. Let a1,a2,a3,... be in harmonic progression with a1=5a n da(20)=25. ...

    Text Solution

    |

  8. An infinite G.P. has first term as a and sum 5, then a belongs to a) |...

    Text Solution

    |

  9. Let Ssub(0,pi) denote the set of values of x satisfying the equation 8...

    Text Solution

    |

  10. The value of sum(r=0)^n(a+r+a r)(-a)^r is equal to a.(-1)^n[(n+1)a^(n+...

    Text Solution

    |

  11. If x1,x2 …,x(20) are in H.P and x1,2,x(20) are in G.P then underset(r=...

    Text Solution

    |

  12. The sum of series x/(1-x^2)+(x^2)/(1-x^4)+(x^4)/(1-x^8)+ to infinite t...

    Text Solution

    |

  13. If bi=1-ai ,n a=sum(i=1)^n ai ,n b=sum(i=1)^n bi ,t h e nsum(i=1)^n ai...

    Text Solution

    |

  14. The greatest integer by which 1+sum(r=1)^(30)rxxr ! is divisible is a....

    Text Solution

    |

  15. (lim)(ntooo)sum(r=1)^n r/(1xx3xx5xx7xx9xxxx(2r+1)) is equal to 1/3 b. ...

    Text Solution

    |

  16. Value of (1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))........oo is equal ...

    Text Solution

    |

  17. If sum(r=1)^n r^4=I(n),t h e nsum(r=1)^n(2r-1)^4 is equal to a. I(2n)-...

    Text Solution

    |

  18. If sum of an infinite G.P. : p ,1,1//p ,1//p^2, ........ is 9//2 then ...

    Text Solution

    |

  19. The sum of i-2-3i+4 up to 100 terms, where i=sqrt(-1) is 50(1-i) b. 2...

    Text Solution

    |

  20. If a1, a2, a3, ,a(2n+1) are in A.P., then (a(2n+1)-a1)/(a(2n+1)+a1)+(...

    Text Solution

    |