Home
Class 11
MATHS
Find two positive numbers whose differen...

Find two positive numbers whose difference is 12 an whose A.M. exceeds the G.M. by 2.

Text Solution

Verified by Experts

Let the two numbers be a and b.
Then, `a − b = 12 … (i) `
It is given that
` A.M. – G.M. = 2`
...
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|157 Videos
  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|5 Videos

Similar Questions

Explore conceptually related problems

Find two numbers whose difference is 2 and product is 24.

Find two positive numbers whose sum is 16 and product is maximum.

Find two positive numbers whose sum is 14 and product is maximum.

Find two positive numbers whose product is 64 and the sum is minimum.

Find two positive numbers whose product is 49 and the sum is minimum.

The A.M. between two positive numbers exceeds the GM by 5, and the GM exceeds the H.M. by 4. Then the numbers are-

Find the two odd numbers whose sum is 12.

Find two numbers whose A.M. is 34 and G.M. is 16.

Find two positive numbers a and b whose AM and GM are 34 and 16 respectively.

Find two positive numbers a and b, whose (i) AM = 25 and GM = 20 (ii) AM = 10 and GM = 8.

RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. Insert 5 geometric means between 576 and 9.

    Text Solution

    |

  2. Let x be the arithmetic mean and y ,z be tow geometric means between a...

    Text Solution

    |

  3. Find two positive numbers whose difference is 12 an whose A.M. exce...

    Text Solution

    |

  4. If one geometric mean G and two arithmetic means A1a n dA2 be inserted...

    Text Solution

    |

  5. If a is the A.M. of ba n dc and the two geometric means are G1a n dG2 ...

    Text Solution

    |

  6. If x in R , find the minimum value of the expression 3^x+3^(1-x)dot

    Text Solution

    |

  7. If x ,y ,z are distinct positive numbers, then prove that (x+y)(y+z)(z...

    Text Solution

    |

  8. If a ,b ,c are in G.P. then prove that (a^2+a b+b^2)/(b c+c a+a b)=(b+...

    Text Solution

    |

  9. If 1/(a+b),1/(2b),1/(b+c) are three consecutive terms of an A.P., prov...

    Text Solution

    |

  10. If a ,b ,c ,d are in G.P. prove that: (a b-c d)/(b^2-c^2)=(a+c)/b

    Text Solution

    |

  11. If a ,b ,c ,d are in G.P. prove that: (a^2+b^2),(b^2+c^2),(c^2+d^2) ar...

    Text Solution

    |

  12. The sum of three numbers a ,b ,c in A.P. is 18 . If a and b are each i...

    Text Solution

    |

  13. If a ,b ,c are in G.P., prove that: 1) a(b^2+c^2)=c(a^2+b^2) , 2)...

    Text Solution

    |

  14. If mth, nth and pth terms of a G.P. form three consecutive terms of a ...

    Text Solution

    |

  15. If a ,b ,c are in G.P. and x ,y are the arithmetic means of a ,ba n db...

    Text Solution

    |

  16. If x^a=x^(b//2)z^(b//2)=z^c , then prove that 1/a ,1/b ,1/c are in A.P...

    Text Solution

    |

  17. If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , t...

    Text Solution

    |

  18. If the sum of three numbers in G.P. is 38 and their product is 1728, ...

    Text Solution

    |

  19. If the p^(t h) and q^(t h) terms of a G.P. are q and p respectively, s...

    Text Solution

    |

  20. In a finite G.P. the product of the terms equidistant from the begi...

    Text Solution

    |