Home
Class 11
MATHS
The sum of the squares of three distinct...

The sum of the squares of three distinct real numbers, which are in GP is `S^2`. If their sum is `alphaS` , show that `alpha ^2in(1/3,1)uu(1,3)`.

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos
  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

Sum of the square of three different terms, which are in GP is s^2 . If the sum of the three terms is alpha s, show that 1/3< alpha^2 <3.

If sum of the square of three different terms in G.P. is S^(2) their sum is alpha S , then show that (1)/(3) lt alpha^(2) lt 3 .

If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , then prove that either x 3.

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

The sum of three consecutive numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.

For three distinct positive numbers a, b, c with a + b + c = 1, show that 8abc le (2/3)^3 .

The sum of three numbers of GP is 39/10 and their product is 1. Find the numbers.

The common ratio of a series in G.P. is 3, the sum of the 1st and 3rd terms is equal to the sum of the squares of the 1st and 2nd terms, find the sum of n terms. If n = 6, show that the sum is 364.

The number of distinct real root of x^3-3x+1=0 in (1,2) is

If S_1, S_2, S_3 are the sum of first n natural numbers, their squares and their cubes, respectively , show that 9 S_(2)^(2) = S_(3) (1+ 8S_1)

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Find the sum of the first n terms of the series 1^3+3.2^2+3^3+3.4^2+5^...

    Text Solution

    |

  2. Does there exist a GP containing 27,8 and 12 as three of its terms ? I...

    Text Solution

    |

  3. The sum of the squares of three distinct real numbers, which are in GP...

    Text Solution

    |

  4. Prove that the three successive terms of a GP will form the sides of ...

    Text Solution

    |

  5. If (m+1)^th ,(n+1)^th and (r+1)^th terms in AP are in GP m,n,r are in ...

    Text Solution

    |

  6. If p be the first of n arithmetic means between two numbers and q be t...

    Text Solution

    |

  7. Show that 1^4/13+2^4/3.5+3^4/5.7+.....+n^4/((2n-1)(2n+1))=(n(4n^2+6n+5...

    Text Solution

    |

  8. Solve the following equations for x and y log10xx+1/2log10xx+1/4log10x...

    Text Solution

    |

  9. Find the sum of the series 1/1.3+2/(1.3.5)+3/(1.3.5.7)...upto infinit...

    Text Solution

    |

  10. If sum(r=1)^nTr =n/8(n+1)(n+2)(n+3) then find sum(r=1)^n1/Tr

    Text Solution

    |

  11. If 1,log9(3^(1-x)+2) and log3(4.3^x-1) are in AP , then x is equal to

    Text Solution

    |

  12. If the sum of the first 2n terms of the AP 2,5,8.....is equal to the s...

    Text Solution

    |

  13. If xin R , the number 5^(1+x)+5^(1-x),a/2,25^x+25^-xform an AP , then ...

    Text Solution

    |

  14. If an AP a7=9 and a1a2a7 is least , then common difference is

    Text Solution

    |

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

    Text Solution

    |

  16. The value of a^(logb(x))=(where, a=0.2,b=sqrt5), x=(1/4+1/8+1/16+........

    Text Solution

    |

  17. If a,b,c are in HP and agtcgt0, then 1/(b-c)-1/(a-b).

    Text Solution

    |

  18. Let the positive numbers a,b,c,d be in AP , Then abc, abd,acd,bcd are

    Text Solution

    |

  19. If a,b,c are in HP , thn the value of (b+a)/(b-a)+(b+c)/(b-c) is

    Text Solution

    |

  20. If x1gt0,i=1,2.....50 and x1+x2+.....x50=50 then the minimum value of ...

    Text Solution

    |