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
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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
由题意2x*2Y=1且x,y均为正数,即xy=1/4.设x+y=a(a>0)
又x^4+y^4=194即(a^2-2xy)^2-2x^2*y^2=194得a=3.799