Home
Class 11
MATHS
Let x,y,z be real variable satisfying th...

Let x,y,z be real variable satisfying the equations x+y+z=6 and xy+yz+zx=7. Then find the range in which the variable can lie.

Text Solution

Verified by Experts

`[(6-2sqrt15)/2,(6+2sqrt15)/3]`
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

  • RECTANGULAR CO-ORDINATES

    PATHFINDER|Exercise QUESTION BANK|27 Videos

Similar Questions

Explore conceptually related problems

Let x and y be two real variable such that x >0 and x y=1 . Find the minimum value of x+y .

Let x ,y ,z in R such that x+y+z=5 and x y+y z+z x=3. Thenwhat is the largest value x can have?

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.

If x^2+y^2+z^2= xy+yz+zx then find the value of (x+y):z.

Let x, y be real variable satisfying the x^2 + y^2 + 8x - 10 y - 40 = 0 Let a = max{(x + 2)^2 + (y - 3)^2} and b = min{(x + 2)^2 + (y - 3)^2} , then

If x prop yz and y prop zx, then prove that z is a non- zero variation constant.

If the relation between two variable x and y is 5y+7x=11 and the range of x is 5, then the range of y is _______ .

If x^2 prop yz ,y^2 prop zx and z^2 prop xy , then find the product of three variation constant

The variables srideepa and tasmir can be fused to give rise to another variable aneesh, with the relation xy=z

If x,y,z are positive real numbers such that x^(2)+y^(2)+Z^(2)=7 and xy+yz+xz=4 then the minimum value of xy is

PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. If P(x) = ax^2+bx+c, and Q(x) = -ax^2+dx+c, acne 0, then prove that P(...

    Text Solution

    |

  2. If,alpha be the root of equation ax^2+bx+c=0 and beta be root of -ax^2...

    Text Solution

    |

  3. Let x,y,z be real variable satisfying the equations x+y+z=6 and xy+yz+...

    Text Solution

    |

  4. If one root of the quadratic equation ax^2+bx+c=0 is equal to the n^th...

    Text Solution

    |

  5. Find all real values of a for which the equation x^4+(a-1)x^3+x^2+(a-...

    Text Solution

    |

  6. Solve the equation (x+2)(x+3)(x+8)(x+12)=4x^2

    Text Solution

    |

  7. Solve the equation x^(logx(x+3)^2 )=16

    Text Solution

    |

  8. If x is real, find the values of k for which abs(x^2+kx+1)/abs(x^2+x+1...

    Text Solution

    |

  9. Let S be the set of all non-zero real numbers alpha such that the quad...

    Text Solution

    |

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

    Text Solution

    |

  11. If alpha,beta are the roots of x^2-px+1=0 and gamma is a root of x^2+p...

    Text Solution

    |

  12. The quadratic expression (2x+1)^2-px+qne0 for any real x if

    Text Solution

    |

  13. Given that x is a real number satisfying (5x^2-26x+5)/(3x^2-10x+3)lt0,...

    Text Solution

    |

  14. Let f : R to R be defined as f(x) =(x^2-x+4)/(x^2+x+4). Then the range...

    Text Solution

    |

  15. If 2 + i and sqrt5-2i are the roots of the equation (x^2+ax+b)(x^2+cx+...

    Text Solution

    |

  16. Which of the following is/are always false ?

    Text Solution

    |

  17. The quadratic equations p(x) =0 with real coefficients has purely imag...

    Text Solution

    |

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

    Text Solution

    |

  19. Let alpha and beta be the roots of equation px^2+qx+r=0,pne0. If p, q,...

    Text Solution

    |

  20. In a Delta ABC, tanA and tanB are roots of pq(x^2+1)=r^2x. Then DeltaA...

    Text Solution

    |