<prompt> Kuna nambari kamili a,b, na c chanya kama hizo3 sqrtsqrt35 - sqrt34 sqrt3a sqrt3b - sqrt3c .Tafuta a b c.  <response>: Kupiga pande zote mbili, tunapata9 sqrt35 - 9 sqrt34 sqrt3a2 sqrt3b2 sqrt3 c2 2 sqrt3ab - 2 sqrt3ac - 2 sqrt3bc.Ili kufanya upande wa kulia ufanane na upande wa kushoto, baadhi masharti pengine itabidi kughairi.Tuseme sqrt3a2 2 sqrt3bc. Kisha a2 8bc, hivyo c fraca28b. Inabadilisha , upande wa kulia unakuwaanzaalignsqrt3b2 sqrt3fraca464b2 2 sqrt3ab - 2 sqrt3a cdot fraca28b sqrt3b2 fraca4b sqrt3ab 2 sqrt3ab - fracab sqrt3b2 kushoto 1 - fracab kulia sqrt3b2 kushoto fraca4b 2 kulia sqrt3 ab.endalignKwa wakati huu, tunaweza kujaribu kuwa na utaratibu, lakini ni rahisi kujaribu baadhi ya thamani ndogo. Kwa mfano, tunaweza kujaribu kuchukua b 2, ili kunasa neno sqrt34. Hii inatupakushoto 1 - fraca2 kulia sqrt34 kushoto fraca8 2 kulia sqrt32a .Kisha kuchukua a 20 hutupatia kile tunachotaka:kushoto 1 - frac202 kulia sqrt34 kushoto frac208 2 kulia sqrt340 9 sqrt35 - 9 sqrt34.Kisha c fraca28b 25. Hivyo, a b c 20 2 25 47. 