Home
Class 10
MATHS
If x1 and x2be any two positive variabl...

If `x_1` and `x_2`be any two positive variables and if the arithmetic mean of these two values be A, geometric mean be G and harmonic mean be H, then peove that `G^2 = AH`

Text Solution

Verified by Experts

`100*89 (approx )
Promotional Banner

Topper's Solved these Questions

  • RIGHT CIRCULAR CYLINDER

    CALCUTTA BOOK HOUSE|Exercise Exercise - 2 (Long-answer type questions)|11 Videos

  • SIMILARITY

    CALCUTTA BOOK HOUSE|Exercise Exercise 5.2|27 Videos

Similar Questions

Explore conceptually related problems

If two positive values of a variable be x_(1) and x_(2) and the arithmetic mean be A, geometric mean be G and the harmonic mean be H, then prove that G^(2)=AH

The arithmetic mean of two numbers is 10 and their geometric mean is 8. find the numbers.

If the arithmetic mean of two numbers be 10 and their harmonic mean is 7.5 , then what are two numbers ?

The two geometric means between 1 and 64 are-

The arithmetic mean of the numbers 1, 2, 3, ...., n is

Find the geometric mean between 2a and 8a^3

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

The arithmetic mean of 1, 2, 3, ……., n is___

If the arithmetic mean of two positive numbers a & b (a gt b) is twice their geometric mean , then a : b is

x and y are two variables, such that y = (3)^(1/x) . If the harmonic mean of x is 3, find the geometric mean of y.

CALCUTTA BOOK HOUSE-SAMPLE QUESTIONS PAPERS-QUESTION
  1. The tens' digit of a two digit number is less by 3 than the unit digit...

    Text Solution

    |

  2. The price of a diamond is ₹ 2000. The diamond is broken into two pies...

    Text Solution

    |

  3. If x=3+2sqrt2, then find the value of (sqrtx -""1/sqrtx)

    Text Solution

    |

  4. If a+1/b = 1 and b+1/c=1 then prove that c+1/a =1

    Text Solution

    |

  5. If a, b, c be in continued proportional, then prove that a^2 b^2 c^2 (...

    Text Solution

    |

  6. Prove that angles in the same segment of a circle are equal.

    Text Solution

    |

  7. Prove that if two tangents are drawn to a circle from a point outside ...

    Text Solution

    |

  8. ABCD is a parallelogram. A circle passing through C and D intersects A...

    Text Solution

    |

  9. Construct a circle of radius 2*6cm. Take a point outside of this circl...

    Text Solution

    |

  10. The length of radius of a circle is 21 cm. Determine the cfircular and...

    Text Solution

    |

  11. Find the value : (tan^2 60^@+tan30^@)/(1+tan^2 60^@+tan30^@)+cos 60^@ ...

    Text Solution

    |

  12. If /A + /B = 90^@ then prove that 1+(tan A)/(tan B) = "cosec"^2 B

    Text Solution

    |

  13. If the angle of elevation of the top of a chimney from a point on the ...

    Text Solution

    |

  14. If the angle of depression of two consecutive kilometer stones on a ro...

    Text Solution

    |

  15. How many solid sphere of radius 10*5 cm each can be mad by melting a s...

    Text Solution

    |

  16. To prepare a tent of shaped a right circular cone, it needs 77 sq-metr...

    Text Solution

    |

  17. The external diameter of a gold - sphere is 12 cm and it is made of a ...

    Text Solution

    |

  18. If x1 and x2be any two positive variables and if the arithmetic mean ...

    Text Solution

    |

  19. prove thatsqrt108 -sqrt75=sqrt3

    Text Solution

    |

  20. Find the addition of (2+sqrt3) and (2-sqrt3)

    Text Solution

    |