Home
Class 11
MATHS
If the terms of the A.P, sqrt(a-x),sqrt...

If the terms of the A.P, `sqrt(a-x),sqrt(x),sqrt(a+x)` are all in integers, where `a>x >0,` then find the least composite value of `a`.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

Find the range of f(x) = sqrt(x-1)+sqrt(5-x)

If f(x)=sqrt(x^2+a x+4) is defined for all x , then find the value of adot

For a ,x ,>0 prove tht at most one term of the G.P. sqrt(a-x),sqrt(x),sqrt(a+x) can be rational.

The value of lim_(x to oo) sqrt(x)(sqrt(x+2)-sqrt(x)) is -

Find the range of f(x)=sqrt(x-1)+sqrt(5-x)

Find all possible values of sqrt(|x|-2)

Evaluate lim_(xtooo) sqrt(x)(sqrt(x+c)-sqrt(x)).

If x= 3+ 2sqrt2 then find the value of x+1/x .

The value of int (a^(sqrt(x)))/(sqrt(x))dx is -

sqrt6xx sqrt15=xsqrt10 .then find the value of x.

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Find the sum of first 10 evenwhole number.

    Text Solution

    |

  2. Find the sum of the natural numbers less than 100, which are divisible...

    Text Solution

    |

  3. If the terms of the A.P, sqrt(a-x),sqrt(x),sqrt(a+x) are all in integ...

    Text Solution

    |

  4. For a ,x ,>0 prove tht at most one term of the G.P. sqrt(a-x),sqrt(x),...

    Text Solution

    |

  5. If 1/1^2+1/2^2+1/3^2+.... upto infty=pi^2/6 , then, find 1/1^2+1/3^2+1...

    Text Solution

    |

  6. Coefficient of x^(18) in (1+x+2x^2+3x^3++18 x^(18))^2 equal to 995 b. ...

    Text Solution

    |

  7. Let alpha , beta be the roots of x^2-x+p=0 and gamma,delta be the root...

    Text Solution

    |

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

    Text Solution

    |

  9. Statement 1: If the arithmetic mean of two numbers is 5/2 geometric ...

    Text Solution

    |

  10. Number of positive integral ordered pairs of (x,y), so that 8,x,y are ...

    Text Solution

    |

  11. If three positive real numbers a,b ,c are in A.P such that a b c=4 , t...

    Text Solution

    |

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

    Text Solution

    |

  13. The maximum sum of the series 20+19 1/3+18 2/3+...... is (A) 310 (B) ...

    Text Solution

    |

  14. The sum of n terms of a progression is (2^n-1). Show that it is a GP a...

    Text Solution

    |

  15. Let a1 , a2 ,... be in harmonic progression with a1 = 5 and a20 = 25. ...

    Text Solution

    |

  16. An infinite G.P. has first term as a and sum 5, then a belongs to a) |...

    Text Solution

    |

  17. Let Ssub(0,pi) denote the set of values of x satisfying the equation 8...

    Text Solution

    |

  18. Find the number of terms of a G.P. whose first term is ¾, common ratio...

    Text Solution

    |

  19. In an A.P. (with usual notations) : (i) given a = 7, a13 = 35, find ...

    Text Solution

    |

  20. Find the geometric progression whose 4th term is 54 and the 7th term i...

    Text Solution

    |