设2sin&+cos&=x ① sin&+2cos&=2②
①²+②²=5（sin&）²+5（cos&）²+8sin&cos&=4+x² 即sin&cos&=(x²-1)/8
①×②=2（sin&）²+2（cos&）²+5sin&cos&=2x 即sin&cos&=(2x-2)/5
∴(x²-1)/8=(2x-2)/5 解得x=1或x=11/5