Home
Class 11
MATHS
Let x^2+y^2+x y+1geqa(x+y)AAx ,y in R ,...

Let `x^2+y^2+x y+1geqa(x+y)AAx ,y in R ,` then the number of possible integer (s) in the range of `a` is___________.

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If R={(x,y):x inNN,y in NN and x+2y=8} , then the number of elements of R will be____

If R={(x,y): x,y in W, x ^(2)+y^(2)=25} , then find the domain and range of R.

Let y be an element of the set A={1,2,3,4,5,6,10,15,30} and x_(1) , x_(2) , x_(3) be integers such that x_(1)x_(2)x_(3)=y , then the number of positive integral solutions of x_(1)x_(2)x_(3)=y is

If x, y, z are integers such that x ge 0, y ge 1, z ge 2 and x + y + z = 15, then the number of ordered triplets of the from (x,y,z) is

If x,y,z, in R such that x+y+z=4, x^2+y^2+z^2=6 then find the range of x.

Let f(x+y)=f(x)+f(y)+2xy-1 AAx,yinRR, If f(x) is differentiable and f'(0) = sin phi then -

If f(x+y)=f(x)+f(y)-x y-1AAx , y in R and f(1)=1, then the number of solution of f(n)=n , n in N , is 0 (b) 1 (c) 2 (d) more than 2

Find the number of redered pairs (x,y) satisfying x^2+1=y and y^2+1=x

If (y^2-5y+3)(x ^2+x+1)<2x for all x in R , then find the interval in which y lies.

If R ={(x,y) :x is an integer and |x| lt 3 "and" y=|x-3|} then the range of R is

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If omega is an imaginary fifth root of unity, then find the value of ...

    Text Solution

    |

  2. a ,b ,a n d c are all different and non-zero real numbers on arithmet...

    Text Solution

    |

  3. Let x^2+y^2+x y+1geqa(x+y)AAx ,y in R , then the number of possible i...

    Text Solution

    |

  4. If alpha=e^(i2pi//7)a n df(x)=a0+sum(k=0)^(20)ak x^k , then prove that...

    Text Solution

    |

  5. If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition tha...

    Text Solution

    |

  6. If z is a non real root of root(7)(-1) , then find the value of z^(86...

    Text Solution

    |

  7. The quadratic equation x^2+m x+n=0 has roots which are twice those of ...

    Text Solution

    |

  8. Let omega=-1/2+i(sqrt(3))/2dot Then the value of the determinant |1 1 ...

    Text Solution

    |

  9. All the value of k for which the quadratic polynomial f(x)=2x^2+k x+2=...

    Text Solution

    |

  10. ifa=cos(2pi//7)+isin(2pi//7) , then find the quadratic equation whose ...

    Text Solution

    |

  11. Let complex numbers alpha and 1/alpha^- lie on circles (x-x0)^2+(y-y0...

    Text Solution

    |

  12. If |z/| barz |- barz |=1+|z|, then prove that z is a purely imaginary ...

    Text Solution

    |

  13. If x=-5+2sqrt(-4) , find the value of x^4+9x^3+35 x^2-x+4.

    Text Solution

    |

  14. Let a , b ,a n dc be rel numbers which satisfy the equation a+1/(b c)=...

    Text Solution

    |

  15. The value of i^(1+3+5+.....+(2n+1)) is.

    Text Solution

    |

  16. a ,b , c are integers, not all simultaneously equal, and omega is cube...

    Text Solution

    |

  17. a, b, c are reals such that a+b+c=3 and   1/(a+b)+ 1/(b+c) + 1/ (c+...

    Text Solution

    |

  18. If z + 1/z = 2costheta, prove that |(z^(2n)-1)//(z^(2n)+1)|=|tannthet...

    Text Solution

    |

  19. If alpha,beta are the roots of the quadratic equation a x^2+b x+c=0 , ...

    Text Solution

    |

  20. The locus represented by the equation abs(z-1)=abs(z-i) is

    Text Solution

    |