设ABC为正数,且满足A^+B^=C^,若log4(1+[B+C]\A)=1,log8(A+B-C)=2\3,ABC是个是多少

设ABC为正数,且满足A^+B^=C^,若log4(1+[B+C]\A)=1,log8(A+B-C)=2\3,ABC是个是多少
设ABC为正数,且满足A^+B^=C^,若log4(1+[B+C]\A)=1,log8(A+B-C)=2\3,ABC是个是多少

设ABC为正数,且满足A^+B^=C^,若log4(1+[B+C]\A)=1,log8(A+B-C)=2\3,ABC是个是多少
log4(1+[B+C]\A)=1=log4(4)
==>1+[B+C]/A=4
==>3A=B+C
log8(A+B-C)=2\3=log8(4)
==>A+B-C=4
==>B=A+2,C=2(A-1)
A^2+B^2=C^2
==>2A^2-12A=0
==>A=6
==>A=6,B=8,C=10