<prompt> Acha x sqrtfracsqrt532 frac32. Kuna nambari kamili chanya a, b, c za kipekee ambazox100 2x98 14x96 11x94 - x50 shoka46 bx44 cx40. Tafuta a b c.  <response>: Tuna hiyo x2 fracsqrt532 frac32. Kisha 2x2 sqrt53 3, hivyo 2x 2 - 3 sqrt53. Kuweka pande zote mbili, tunapata4x4 - 12x2 9 53,hivyo 4x4 12x2 44. Kisha x4 3x2 11.Kwa kuwa x neq 0, tunaweza kugawanya pande zote mbili za mlinganyo uliotolewa kwa x40, ili kupatax60 2x58 14x56 11x54 - x10 ax6 bx4 c.Sasa,anzaalignx60 - 2x58 - 14x56 - 11x54 x54 x6 - 2x4 - 14x2 - 11 x54 x2 - 2 x4 - 14x2 - 11 x54 x2 - 23x2 11 - 14x2 - 11 x54 3x4 - 9x2 - 33 3x54 x4 - 3x2 - 11 0.endalignKwa hivyo, mlinganyo unapungua hadix10 ax6 bx4 c.Tunayo hiyoanzaalignx6 x2 cdot x4 x2 3x2 11 3x4 11x2 33x2 11 11x2 20x2 33, x8 x2 cdot x6 x2 20x2 33 20x4 33x2 203x2 11 33x2 93x2 220, x10 x2 cdot x8 x2 93x2 220 93x4 220x2 933x2 11 220x2 499x 2 1023.endalignHivyo, x10 ax6 bx4 c inakuwa499x2 1023 a20x2 33 b3x2 11 c.Kisha499x2 1023 20a 3bx2 33a 11b c.Kwa kuwa x2 haina mantiki, tunataka a, b, na c ili kukidhi 20a 3b 499 na 33a 11b c 1023. Kutatua kwa a na b, tunapataa frac3c 2420121, quad b frac3993 - 20c121.Kwa hivyo, c frac399320, ambayo inamaanisha c le 199. Pia, tunataka 3c 2420 iweze kugawanywa na 121 Kwa kuwa 2420 inaweza kugawanywa na 121, c lazima igawanywe kwa 121. Kwa hiyo, c 121, ambayo ina maana a 23 na b 13, hivyo a b c 157. 