Home
Class 14
MATHS
If x^(2)+y^(2)+z^(2)=a, then prove th...

If `x^(2)+y^(2)+z^(2)=a`,
then prove that value of `xy+yz +zx` lies between `(-a)/(2) and a`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ALGEBRAIC IDENTITIES

    LUCENT PUBLICATION|Exercise Exercise - 1A |104 Videos

  • ALGEBRAIC IDENTITIES

    LUCENT PUBLICATION|Exercise Exercise - 1B|28 Videos

  • ADVANCED TRIGONOMETRIC IDENTITIES

    LUCENT PUBLICATION|Exercise EXERCISE 13A|49 Videos

  • CENTRE OF TRIANGLE

    LUCENT PUBLICATION|Exercise EXERCISE-6B|8 Videos

Similar Questions

Explore conceptually related problems

If x+y+z =10 , x^(2) +y^(2) +z^(2) =60 then value of xy+yz +zx is

If x^(2)+y^(2)+z^(2)=1 then xy+yz+zx lies in

If x^(2) + y^(2) + z^(2) = xy + yz + zx , then the triangle is :

If (x^(2)+y^(2)+z^(2)-64)/(xy-yz-zx)=-2 and x+y=3z, then the value of z is (a) 2 (b) 3 (c) 4 (d) None of these

If x + y + z = 0 , then the value of (x^2)/(yz) + (y^2)/(zx) + (z^2)/(xy) is:

If x^2 + y^2 + z^2 = xy + yz + zx , then the triangle is :

If tan^(-1)x+tan^(-1)y+tan^(-1)z=(pi)/(2), prove that xy+yz+zx=1

If tan^(-1)x+tan^(-1)y+tan^(-1)z=(pi)/(2) then prove that yz+zx+xy=1

LUCENT PUBLICATION-ALGEBRAIC IDENTITIES -Exercise - 1B
  1. If x^(2)+y^(2)+z^(2)=a, then prove that value of xy+yz +zx lies bet...

    Text Solution

    |

  2. If a+b+1=0 then what is the value of (a^(3)+b^(3)+1-3ab)?

    Text Solution

    |

  3. If x=(0.08)^(2), y=(1)/((0.08)^(2)) and z=(1-0.08)^(2)-1 then which of...

    Text Solution

    |

  4. If x^(4)+(1)/(x^(4))=23 then what is the value of (x-(1)/(x))^(2)?

    Text Solution

    |

  5. If x+(1)/(x)=3 then what is the value of x^(5)+(1)/(x^(5)) ?

    Text Solution

    |

  6. If a+b=6, a-b=2 then what is the value of 2(a^(2)+b^(2))?

    Text Solution

    |

  7. If 2a-(2)/(a)+3=0, then value of (a^(3)-(1)/(a^(3))+2) is -

    Text Solution

    |

  8. If factors of x^(3)+(a+1) x^(2)-(b-2)x -6 are (x+1) and (x-2) then val...

    Text Solution

    |

  9. If x is real and x^(4)+(1)/(x^(4))=119, then value of (x-(1)/(x)) is

    Text Solution

    |

  10. If x^(3) + y^(3) = 35 and x + y = 5 then the value of (1)/( x) + (...

    Text Solution

    |

  11. If (x^(2))/(by+cz)=(y^(2))/(cz+ax)=(z^(2))/(ax+by)=1, then value of (a...

    Text Solution

    |

  12. Value of a and b(a gt 0, b lt 0) for which 8x^(3)-ax^(2)+54x+b is a pe...

    Text Solution

    |

  13. If x = ( 4ab)/(a +b) ( a ne b) the value of ( x + 2a)/( x - 2a) + ( x...

    Text Solution

    |

  14. If a+b+c=8, then value of (a-4)^(3) +(b-3)^(3) +(c-1)^(3)-3(a-4) (b-3)...

    Text Solution

    |

  15. If x = sqrt(a) + (1)/( sqrt(a)) , y = sqrt(a) - (1)/( sqrt(a)) ( a gt...

    Text Solution

    |

  16. If 5a+(1)/(3a)=5, then value of 9a^(2)+(1)/(25a^(2)) is

    Text Solution

    |

  17. If a+b+c=0, then what is the value of a^(2)/(bc)+b^(2)/(ca)+c^(2)/(ab)...

    Text Solution

    |

  18. If a, b, c are real, a^(3)+b^(3)+c^(3)=3abc and a+b+c ne 0, then relat...

    Text Solution

    |

  19. If a^(2)+(1)/(a^(2))=98, a gt 0 , then the value of a^(3)+(1)/(a^(3)) ...

    Text Solution

    |

  20. If x+(1)/(x)=5 then what is the value of (x^(4)+(1)/(x^(2)))/(x^(2)-3x...

    Text Solution

    |

  21. If a ^(2) + b ^(2) + c ^(2) = 2 (a - b -c) - 3, then the value of 2a -...

    Text Solution

    |