Home
Class 11
MATHS
If x,y,z, in R such that x+y+z=4, x^2+y^...

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.

Text Solution

Verified by Experts

`[2/3, 2]`
Promotional Banner

Topper's Solved these Questions

  • 3D-GEOMETRY

    PATHFINDER|Exercise QUESTION BANK|39 Videos

  • BINOMIAL THEOREM

    PATHFINDER|Exercise QUESTION BANK|225 Videos

Similar Questions

Explore conceptually related problems

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

Given that x ,y ,z are positive real such that x y z=32. If the minimum value of x^2+4x y+4y^2+2z^2 is equal m , then the value of m//16 is.

If x+y+z=12 and x^2+y^2+z^2=96 and 1/x+1/y+1/z=36 , then find the value of x^3+y^3+z^3

If x : y = 2 : 3 , y : z = 4 : 7 , then find x : y : z .

If R ={ (x,y) : x,y in z, x^(2) +y^(2) le 4 } is a relation on Z Z then domain of R is { 0,-1,k,-2,2} find the value of k.

If z=x+iy and x^(2)+y^(2)=16 , then the range of abs(abs(x)-abs(y)) is

If sin^-1x + sin^-1 y + sin^-1 z = pi , prove that x^4 + y^4 + z^4 + 4x^2y^2z^2 = 2(x^2y^2 + y^2z^2 + z^2x^2)

If x,y,z be variable quantities such that (x+y+z) is constant and (z+x-2y)(x+y-2z) prop yz then show that [2(y+z)-x]propyz .

The x , y , z are positive real numbers such that (log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3, then the value of (1/(2z)) is ............

If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx , y,z are in a. A.P. b. G.P. c. H.P. d. none of these

PATHFINDER-BASIC MATHEMATICS-QUESTION BANK
  1. Solve the following inequalities : sin 3x lt sin x

    Text Solution

    |

  2. Solve the following inequalities : tan^2 x-(1+sqrt3)tan x+ sqrt3lt0

    Text Solution

    |

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

    Text Solution

    |

  4. Complete set of values of x satisfying the inequality x-3 lt sqrt(x^...

    Text Solution

    |

  5. The set of all values of x for which sqrt(-x^2+5x-6)/(sqrt(1-2{x}))ge0...

    Text Solution

    |

  6. The solution of the inequality (abs(x+2)-absx)/sqrt(4-x^3)ge0 is

    Text Solution

    |

  7. Exhaustive set of values of x satisfyinglogabsx(x^2+x+1)ge0 is

    Text Solution

    |

  8. If (log2(4x^2-x-1))/(log2(x^2+1))gt1, then x lies in the interval

    Text Solution

    |

  9. The set of values of x satisfying simultaneously the inequalities sqrt...

    Text Solution

    |

  10. Let alpha=pi/3, then the solution set of the inequality log(sinalpha)(...

    Text Solution

    |

  11. If f(x) =cos[pi^2]x + cos[-pi^2]x, where [x] stands for the greatest i...

    Text Solution

    |

  12. log(0.5)log5(x^2-4)gtlog(0.5)1, then 'x' lies in the interval

    Text Solution

    |

  13. Solution set of the inequality 2- log2(x^2+3x)ge0 is

    Text Solution

    |

  14. Values of x satisfying the equation abs(logsqrt3 x-2)-abs(log3 x-2)=...

    Text Solution

    |

  15. The equation sqrt(x-1)-sqrt(x-1)=sqrt(4x-1) has

    Text Solution

    |

  16. The number of values of x in the interval [0,5pi] satisfying the equat...

    Text Solution

    |

  17. In a Delta PQR,angleR=pi/2. If tan(P/2) and tan (Q/2) are the roots of...

    Text Solution

    |

  18. The number of real roots of 3^(2x^2 -7x+7)=9 is

    Text Solution

    |

  19. The number of the real solutions of the equation x^2-3absx+2=0 is

    Text Solution

    |

  20. If sin(x-y)=cos(x+y)=1/2, then the value of x and y lying between 0 an...

    Text Solution

    |