作业帮设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
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![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](/uploads/image/z/2500817-41-7.jpg?t=%E8%AE%BEABC%E4%B8%BA%E6%AD%A3%E6%95%B0%2C%E4%B8%94%E6%BB%A1%E8%B6%B3A%5E%2BB%5E%3DC%5E%2C%E8%8B%A5log4%281%2B%5BB%2BC%5D%5CA%29%3D1%2Clog8%28A%2BB-C%29%3D2%5C3%2CABC%E6%98%AF%E4%B8%AA%E6%98%AF%E5%A4%9A%E5%B0%91)
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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