log2x+ log2y=0,且x^4+ y^4=194,求log2(x+ y)的值

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log2x+ log2y=0,且x^4+ y^4=194,求log2(x+ y)的值

log2x+ log2y=0,且x^4+ y^4=194,求log2(x+ y)的值
log2x+ log2y=0,且x^4+ y^4=194,求log2(x+ y)的值

log2x+ log2y=0,且x^4+ y^4=194,求log2(x+ y)的值
log2x+ log2y=0,说明xy=1,那么x方y方=1
(x2+y2)2=x4+y4+2x2y2=194+2=196
所以x2+y2=14,14+2xy=(x+y)2=16
所以x+y=4,那么log2(x+ y)=2

log2 x+ log2 y=log2 (xy)=0
xy=1
x^4+ y^4=194
(x^2+y^2)^2-2xxyy=194
(x^2+y^2)^2=196
x^2+y^2=14
(x+y)^2-2xy=14
x+y=4
可得log2 (x+y)=2