Home
Class 11
MATHS
If one A.M 'a' and two GM's p and q be ...

If one A.M 'a' and two GM's p and q be inserted between any two given number, show `p^3+q^3=2apq`.

Promotional Banner

Topper's Solved these Questions

  • SAME SPECIAL SEQUENCE

    PATHFINDER|Exercise QUESTION BANK|28 Videos

  • SET,VENN DIAGRAM AND RELATION

    PATHFINDER|Exercise QUESTION BANK|131 Videos

Similar Questions

Explore conceptually related problems

If one arithmetic mean A and two geometric means p, q be inserted between two given numbers, then prove that, (p^(2))/(q) + (q^(2))/(p) = 2A .

If one geometric mean G and two arithmetic means p, q be inserted between two given numbers, then prove that, G^(2) = (2p - q) (2q - p) .

If x be the AM and y,z be two GM's between two positive numbers, then (y^3 + z^3)/(xyz) is equal to

If P and Q are any two set then P-Q=

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A pm sqrt((A+G )(A−G )) .

Given that n numbers of AMs are inserted between two sets of numbers a, 2b and 2a, b where a,binR . Suppose further that the m th means between these sets of numbers are same, then the ratio a:b equals

If p,q,r are any real number, then

If p be the first of n arithmetic means between two numbers and q be the first of n harmonic means between the same two numbers , then prove that the value of q can not lie between p and ((n+1)/(n-1))^2p .

The A.M. of two numbers is 10, if one number is 7 then the other number will be

The A.M of two numbers is 10,if one number is 7,then the other number will be __

PATHFINDER-SEQUENCES AND SERIES-QUESTION BANK
  1. If the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and ...

    Text Solution

    |

  2. If (a+bx)/(a-bx)=(b+cx)/(b-cx)=(c+dx)/(c-dx) (x+-0) then show a,b,c an...

    Text Solution

    |

  3. Sum to n term .7+.77+.777.......

    Text Solution

    |

  4. The difference between any two consecutive interior angles of a polygo...

    Text Solution

    |

  5. The sum of n term of three A.P are S1,S2,and S3. The frist term of eac...

    Text Solution

    |

  6. If f is a function satisfying f (x +y) = f(x) f(y) for all x, y in N ...

    Text Solution

    |

  7. Find the sum of the following series up to n terms: 1^3/1+(1^3+2^3)/...

    Text Solution

    |

  8. Find the sum of the infinite series 1+(2)/(3)+(3)/(3^2)+(4)/(3^3)+.......

    Text Solution

    |

  9. Find the sum of n terms of the series 3+7+14+24+37+.....

    Text Solution

    |

  10. If the sum of n terms of an A.P. is (pn + qn^2) , where p and q are co...

    Text Solution

    |

  11. If the sum of first p terms of an A.P. is equal to the sum of the firs...

    Text Solution

    |

  12. Evaluate sum(k=1)^11(2+3^k)

    Text Solution

    |

  13. If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively...

    Text Solution

    |

  14. If the first and the n^("th") term of a G.P. are a and b, respectivel...

    Text Solution

    |

  15. Find the sum to n terms of each of the series in 1^2 + (1^2 + 2^2...

    Text Solution

    |

  16. Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3 , respectiv...

    Text Solution

    |

  17. The p th ,q th and r th terms of an A.P are a,b,c respectively. Show t...

    Text Solution

    |

  18. A man saves Rs 32 during frist year Rs.36 in the next year and Rs.40 i...

    Text Solution

    |

  19. If (1)/(x+y),(1)/(2y),(1)/(y+t) are in A.P . Prove that x,y,t are in G...

    Text Solution

    |

  20. If one A.M 'a' and two GM's p and q be inserted between any two given...

    Text Solution

    |