<prompt> Acha a na b ziwe thamani mbili halisi za x ambazosqrt3x sqrt320 - x 2Ndogo kati ya thamani hizo mbili inaweza kuonyeshwa kama p - sqrtq, ambapo p na q ni nambari kamili. Kokotoa p q.  <response>: Acha asqrt3x, b sqrt320-x. Kisha ab 2 na a3 b3 20. Kuanzisha,a3 b3 abab2-3ab 24-3ab 8-6ab20 Longrightarrow ab -2Kutatua ab2, ab-2 inatupa a2 - 2a - 2 0 . Fomula ya quadratic inatoa a frac2 - sqrt122 1 - sqrt3, na x a3 1-sqrt33 1 - 3sqrt3 9 - 3sqrt3 10 - sqrt108. Kwa hiyo, pq118. 