Home
Class 12
MATHS
The harmonic mean of two numbers is 4. T...

The harmonic mean of two numbers is 4. Their arithmetic mean `A` and the geometric mean `G` satisfy the relation `2A+G^2=27.` Find two numbers.

Text Solution

Verified by Experts

The correct Answer is:
(a) 6, 3 (b) 120, 31
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Exercise S-2|12 Videos

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Exercise (JM)|21 Videos

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Exercise O-20|1 Videos

  • RACE

    ALLEN|Exercise Race 21|10 Videos

  • TEST PAPER

    ALLEN|Exercise CHEMISTRY SECTION-II|8 Videos

Similar Questions

Explore conceptually related problems

Find two numbers whose arithmetic mean is 34 and the geometric mean is 16

Find two numbers whose arithmetic mean is 34 and the geometric mean is 16.

The arithmetic mean of two numbers is 6 and their geometric mean G and harmonic mean H satisfy the relation G^(2)+3H=48. Find the two numbers.

The arithmetic mean A of two positive numbers is 8. The harmonic mean H and the geometric mean G of the numbers satisfy the relation 4H + G^(2) = 90 . Then one of two numbers is _____.

The harmonic mean of two positive numbers a and b is 4, their arithmetic mean is A and the geometric mean is G. If 2A+G^(2)=27, a+b=alpha and |a-b|=beta , then the value of (alpha)/(beta) is equal to

The arithmetic mean of two positive numbers is 6 and their geometric mean G and harmonic mean H satisfy the relation G^(2)+3H=48 . Then the product of the two numbers is

ALLEN-SEQUENCE AND PROGRESSION-Exercise S-1
  1. The sum of n terms of two arithmetic series are in the ratio of (7n + ...

    Text Solution

    |

  2. In an AP of which 'a' is the Ist term, if the sum of the Ist p terms i...

    Text Solution

    |

  3. The interior angles of a convex polygon form an arithmetic progression...

    Text Solution

    |

  4. If a gt 0, then minimum value of a + 2a^2+ a^3 + 15+ a^(-1) + a^(-3) +...

    Text Solution

    |

  5. The sequence a(1), a(2), a(3), ..... A(98) satisfies the relation a(n ...

    Text Solution

    |

  6. If A(1), A(2), A(3),....A(51) are arithmetic means inserted between th...

    Text Solution

    |

  7. There are n AM's between 1 & 31 such that 7th mean : (n-1)th mean= 5:9...

    Text Solution

    |

  8. The first term of an arithmetic progression is 1 and the sum of the fi...

    Text Solution

    |

  9. For an increasing G.P. a(1), a(2), a(3),.....a(n), " If " a(6) = 4a(4)...

    Text Solution

    |

  10. In a set of four number, the first three are in GP & the last three ar...

    Text Solution

    |

  11. Find three numbers a, b,c between 2 & 18 such that; O their sum is 25 ...

    Text Solution

    |

  12. If the 10^(th) term of an HP is 21 and 21^(st) term of the same HP is ...

    Text Solution

    |

  13. The pth term Tp, of H.P. is q(p + q) and qth term Tq, is p(p+q) when p...

    Text Solution

    |

  14. The harmonic mean of two numbers is 4. Their arithmetic mean A and the...

    Text Solution

    |

  15. If a, b, c, d gt 0 such that a + 2b + 3c + 4d = 50, then find themaxim...

    Text Solution

    |

  16. If number of coins earned in n^(th) game is n2^(n+2)-2^n and total num...

    Text Solution

    |

  17. Find the n term and the sum to n terms of the sequence: (i) 1+5+13+29+...

    Text Solution

    |

  18. Sum the following series to n terms and to infinity : (i) (1)/(1.4.7...

    Text Solution

    |

  19. Find the value of the sum sum(k =0)^(359) k. cos k^(@)

    Text Solution

    |