已知3^x=4,3^y=6,求9^2x-y+27^x-y

已知3^x=4,3^y=6,求9^2x-y+27^x-y
已知3^x=4,3^y=6,求9^2x-y+27^x-y

已知3^x=4,3^y=6,求9^2x-y+27^x-y
9^(2x-y)+27^(x-y)
=(3²)^(2x-y)+(3³)^(x-y)
=3^(4x-2y)+3^(3x-3y)
=3^4x/3^2y+3^3x/3^3y
=(3^x)^4/(3^y)²+(3^x)³/(3^y)³
=4^4/6²+4³/6³
=256/36+64/216
=64/9+8/27
=192/27+8/27
=200/27

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9^(2x-y)+27^(x-y)
=(3^2)^(2x-y)+(3^3)^(x-y)
=3^(4x-2y)+3^(3x-3y)
=3^4x/3^2y+[3^(x-y)]^3
=(3^x)^4/(3^y)^2+(3^x/3^y)^3
=4^4/6^2+(4/6)^3
=64/9+8/27
=192/27+8/27
=200/27