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minimum value of functionminimum value of when subjected to and satisfies the condition. but I'm not able to show all three at a time I want someone to explain me the problem. |

Re: minimum value of functionBecause of the cyclic symmetry of the variables, the minimum is found when: You will easily find this is true using Lagrange multipliers. |

Re: minimum value of functionI can see , and has similar role, nothing happens if we interchange their position. could u please explain me in simple words. |

Re: minimum value of functionQuote:
at a time". I presume that "all three" refers to minimizing while satisfying x+ y+ z= 1 and xyz= -1. But what do you mean by "at a time"?In any case, what have you tried? |

Re: minimum value of functionwhat I did is, f = x + y + z . . . . (i) x + y + z - 1 = 0 . . . . (ii) xyz + 1 = 0 . . . . (iii) we know, x + y + z = ( x + y + z) - 2xy - 2yz - 2xz f = 1 - 2xy - 2yz - 2xz substituting value of "z" from equation (iii) f = 1 - 2xy + 2/x + 2/y . . . . (vi) partially differentiating equation (vi) w.r.t x and y and equation the results with zero, yx = - 1 . . . . (v) xy = - 1 . . . . (vi) combining (v) and (vi) yx - xy = 0 xy ( x - y ) = 0 thus, x = y why am i getting x = y if x = y, I get only (1, 1, -1) and don't get other point. is the process I followed incorrect ? |

Re: minimum value of function[color=#800040] Mark[/color]there are two conditions, x + y + z - 1 = 0 and xyz + 1 = 0 I don't know latex properly, so may b second condition is not displayed properly. |

Re: minimum value of functionQuote:
[color=#00BF00]HallsofIvy [/color]'s post. In your original post this was not clear. Lagrange multipliers here implies the system:For which we find the real solutions: and: |

Re: minimum value of functionCould u please tell me someone about first three equations. also, mew and lamda. |

Re: minimum value of functionI assumed that if you are studying optimization with constraints, then you are familiar with Lagrange multipliers. I simply do not have the patience with the quirky rendering of here to attempt a tutorial on the subject. |

Re: minimum value of function:'( |

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