<prompt> Mlinganyox1013x-1100,ina mizizi 10 changamano r_1, overliner_1,r_2, overliner _2,r_3, overliner_3,r_4, overliner_4,r_5, overliner_5, ambapo upau unaashiria muunganisho changamano. Tafuta thamani yafrac 1r_1overliner_1frac 1r_2overliner_2frac 1r_3overliner_3frac 1r_4overliner _4frac 1r_5overliner_5.  <response>: Acha px x10 13x - 110. Ikiwa r ni mzizi wa px, basi r10 13x - 110 0. Kisha 13r - 110 -r10, hivyo-1 kushoto frac13r - 1r kulia10 kushoto frac1r - 13 kulia10.Kisha frac1r - 13 ina ukubwa wa 1, kwa hivyokushoto frac1r - 13 kulia kushoto frac1overliner - 13 kulia 1,hivyokushoto frac1r_1 - 13 kulia kushoto frac1overliner_1 - 13 kulia vidoti kushoto frac1 r_5 - 13 kulia kushoto frac1overliner_5 - 13 kulia 5.Kupanua, tunapatafrac1r_1 overliner_1 dots frac1r_5 overliner_5 - 13 kushoto frac1r_1 frac 1 overliner_1 vitone frac1r_5 frac1 overliner_5 kulia 5 cdot 169 5. Tunaona kwamba frac1r_1, frac1overliner_1, dots, frac1r_5, frac 1overliner_5 ndio suluhu zakushoto frac1x kulia10 kushoto frac13x - 1 kulia10 0,au 1 13 - x10 0. Istilahi chache za kwanza katika upanuzi kamax10 - 130x9 dotsb 0,hivyo kwa fomula za Vieta,frac1r_1 frac1overliner_1 dots frac1r_5 frac1overliner_5 130.Kwa hiyo,frac1r_1 overliner_1 dots frac1r_5 overliner_5 13 cdot 130 - 5 cdot 169 5 850. 