Question

若整数a,b,c满足（50/27)a次方x（18/25）b次方x（9/18)=8 求abc 值

Answer 1

5^(2a)*2^a*2^b*3^(2b)*3^(2c)/[3^(3a)*5^(2b)*2^(3c)] =5^(2a-2b)*2^(a+b-3c)*3^(2b+2c-3a) =5^(2a-2b)*2^(a+b-c)*3^(2b+2c-3a) =8=2^3 则a+b-c=3 2a-2b=0 2b+2c-3a=0 解得a=b=2,c=1