<prompt> Acha a, b, c, na d ziwe nambari halisi chanya kiasi kwamba 36a 4b 4c 3d 25. Pata thamani ya juu zaidi yaa mara sqrtb mara sqrt3c mara sqrt4d.  <response>: Na AM-GM,fracunderbrace3a 3a dots 3a_text12 times underbracefrac23 b frac23 b dots frac23 b_text6 times c c c c d d d25 ge sqrt253a 12 kushoto frac23 b kulia6 c4 d3.Hii hurahisishafrac36a 4b 4c 3d25 ge sqrt2546656a12 b6 c4 d3.Tangu 36a 4b 4c 3d 25,a12 b6 c4 d3 le frac146656.Kishasqrt12a12 b6 c4 d3 le frac1sqrt1246656,ambayo inatupaa mara sqrtb mara sqrt3c mara sqrt4d le frac1sqrt6 fracsqrt 66. Usawa hutokea wakati 3a frac23 b c d. Pamoja na hali 36a 4b 4c 3d 25, tunaweza kutatua kupata a frac13, b frac32, c 1, na d 1. Kwa hiyo, thamani ya juu ni frac sqrt66. 