Question

已知整数a,b,c满足20/3的a次方×8/15的b次方×9/16的c次方=4,求a,b,c的值

Answer 1

(20/3)^a×(8/15)^b×(9/16)^c=4

[(2^2×5)/3]^a×[(2^3)/(3×5)]^b×[(3^2)/(2^4)]^c=4

[2^(2a+3b)×3^2c×5^a]/[2^4c×3^(a+b)×5^b]=4

2^(2a+3b-4c)×3^(2c-a-b)×5^(a-b)=2^2

∴2a+3b-4c=2

2c-a-b=0

a-b=0

a=b=c=2