Home
Class 12
MATHS
Find the integral solutions to the equat...

Find the integral solutions to the equation `[x][y]=x+y` . Show that all the non-integral solutions lie on exactly two lines. Determine these lines. Here [.] denotes greatest integer function.

Text Solution

Verified by Experts

The correct Answer is:
Integral solution `(0,0);(2,2).x+y=6,x+y=0`
NA
Promotional Banner

Topper's Solved these Questions

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise SSP|55 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise JEE MAIN|15 Videos

  • NUMBER THEORY

    RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos

  • SEQUENCE & SERIES

    RESONANCE|Exercise EXERCISE -2 (PART-II : PREVIOUSLY ASKED QUESTION OF RMO)|3 Videos

Similar Questions

Explore conceptually related problems

Find out the integral solution for xy=2x-y

Number of solutions of sin x=[x] where [.] denotes the greatest integer function is

Draw the graph of y=[|x|] , where [.] denotes the greatest integer function.

Find the number of positive integral solutions of the equation x+y+z=12.

Find the integral solutions of |x|+|y|+|z|=12.

Find number of negative integral solution of equation x+y+z=-12

Number of solution (s) of the equation sin x=[x][ where [*] denotes greatest integer function is

Find number of solutions for equation [sin^(-1)x]=x-[x] , where [.] denotes the greatest integer function.

RESONANCE-RELATION, FUNCTION & ITF-HLP_TYPE
  1. The period of sin(pi/4)x+cos(pi/2)x+cos(pi/3)x is

    Text Solution

    |

  2. Consider the function g(x) defined as g(x) (x^(2011-1)-1)=(x+1)(x^2+1)...

    Text Solution

    |

  3. It is given that f 9x) is difined on R satisfyinf f (1)=1 and for AA ...

    Text Solution

    |

  4. Find the integral solutions to the equation [x][y]=x+y . Show that all...

    Text Solution

    |

  5. Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C are real numbers. Prove that if...

    Text Solution

    |

  6. Suppose X and Y are two sets and f:XtoY is a function. For a subset A ...

    Text Solution

    |

  7. Let g: Rvec(0,pi/3) be defined by g(x)=cos^(-1)((x^2-k)/(1+x^2)) . The...

    Text Solution

    |

  8. Let 0ltalpha,beta,gammalt(pi)/2 are the solutions of the equations cos...

    Text Solution

    |

  9. Let f(x)=(log)2(log)3(log)4(log)5(s in x+a^2)dot Find the set of value...

    Text Solution

    |

  10. tan^(-1)(tan theta)={(pi+theta,-(3pi)/2lt theta lt -(pi)/2),(theta , -...

    Text Solution

    |

  11. Express cot(cosec^(-1)x) as an algebraic function of x.

    Text Solution

    |

  12. Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1...

    Text Solution

    |

  13. If f(x)=[(x,xlt1),(x^(2),1lexle4),(8sqrt(x),xgt4):} the find f^(-1)(x)...

    Text Solution

    |

  14. sin^(-1)(x^2/4+y^2/9)+cos^(-1)(x/(2sqrt2)+y/(3sqrt2)-2)

    Text Solution

    |

  15. If alpha=2 arc t a n((1+x)/(1-x)) in B=a r c s i n((1-x^2)/(1+x^2))...

    Text Solution

    |

  16. Solve {cos^(-1)x}+[tan^(-1)x]=0 for real values of x. Where {.} and [....

    Text Solution

    |

  17. Find the set of all real values of x satisfying the inequality sec^(-1...

    Text Solution

    |

  18. Find the solution of sin^(-1)(x/(1+x))-"sin"^(-1)(x-1)/(x+1)="sin"^(-1...

    Text Solution

    |

  19. An integral solution of the equation Tan^(-1)x+Tan^(-1)(1//y)=Tan^(-1)...

    Text Solution

    |

  20. Determine the integral values of k for which the system (tan^(-1)x)^(2...

    Text Solution

    |