Home
Class 12
MATHS
Find the greatest and the least real val...

Find the greatest and the least real value of x $ y satisfy the relation `x^2+y^2=6x-8y`.

Text Solution

Verified by Experts

The correct Answer is:
`-2 le x le 8` and `-9lt y le 1`
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE -1 (OBJECTIVE PROBLEMS)|30 Videos

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE -2 (OBJECTIVE PROBLEMS)|28 Videos

  • PERMUTATION AND COMBINATION

    MOTION|Exercise EXAMPLE|23 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -4 Level -II Previous Year /JEE Advanced|22 Videos

Similar Questions

Explore conceptually related problems

Find the values of x and y which satisfy the equations: y+4x=9 and 3y+2x=5

Find the greatest value of x, which satisfies the system of equations : x^(3)+y^(3)=35,x^(2)y+xy^(2)=30 .

Find the greatest value of c such that system of equation x^(2) + y^(2)=25, x+y =c has a real solution

Find the least and the greatest value of f(x , y) = x^(2) + y^(2) - xy where x and y are connected by the relation x^(2) + 4y^(2) = 4

Find the smallest positive value of x and y satisfying x-y=(pi)/(4) and cot x+cot y=2

Find the greatest and least value of y= x^(3)-3x^(2) + 6x-2 on [-1,1] y is differentiable function of x and y'(x) = 3x^(2) -6x + 6= 3(x^(2) -2x+2) =3(x-1)^(2) gt 0 .

Find all ordered pairs of real numbers that satisfy both the equations x^(2)+y^(2)=2xy and x^(2)+y^(2)=6x+6y+2

Find the smallest positive values of x and y satisfying x-y=(pi)/(4) and cot x+cot y=2

Find the greatest &x least value for the function; y=x+sin2x,0<=x<=2 pi

MOTION-QUADRATIC EQUATION-EXERCISE 4 (PREVIOUS YEAR| JEE MAIN)
  1. Find the greatest and the least real value of x $ y satisfy the relati...

    Text Solution

    |

  2. If the difference between the roots of the equation x^2+""a x""+""1...

    Text Solution

    |

  3. The quadratic equations x^2""6x""+""a""=""0""a n d""x^2""c x""+""6"...

    Text Solution

    |

  4. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

    Text Solution

    |

  5. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, ...

    Text Solution

    |

  6. If a and b are the roots of the equation x^2""x""+""1""=""0 , then alp...

    Text Solution

    |

  7. 8. Sachin and Rahul attempted to solve a quadratic equation. Sachin ma...

    Text Solution

    |

  8. Show that the equation e^(sinx)-e^(-sinx)-4=0 has no real solution.

    Text Solution

    |

  9. The real number k for which the equation, 2x^3+""3x""+""k""=""0 has tw...

    Text Solution

    |

  10. If the equation x^(2)+2x+3=0 and ax^(2)+bx+c=0, a,b,c in R have a comm...

    Text Solution

    |

  11. Let alpha and beta be the roots of equation px^2 + qx + r = 0 , p != ...

    Text Solution

    |

  12. If a in R and the equation -3(x-[x])^2+2(x-[x])+a^2=0 (where [x] denot...

    Text Solution

    |

  13. Let alpha and beta be the roots of equation x^2-6x-2""=""0 . If an=...

    Text Solution

    |

  14. alpha,beta be the roots of the equation x^2-px+r=0 and alpha/2 , 2beta...

    Text Solution

    |

  15. Let f(x)=(x^(2)-6x+5)/(x^(2)-5x+6) Match the expressions/ statements i...

    Text Solution

    |

  16. Let a,b,c,p,q be the real numbers. Suppose alpha,beta are the roots of...

    Text Solution

    |

  17. The smallest value of k, for which both the roots of the equation, x^2...

    Text Solution

    |

  18. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

    Text Solution

    |

  19. Let alpha and beta be the roots of x^2-6x-2=0 with alpha>beta if an=al...

    Text Solution

    |

  20. A value of b for which the equation x^2+b x-1=0,x^2+x+b=0 have one roo...

    Text Solution

    |

  21. Let a in R and let f: R to R be given by f(x) =x^(5) -5x+a. then

    Text Solution

    |