a,b∈R,且x=y的平方,求证log以2为底真数为2的x次方+2的y次方＞8分之7

x=y²2^x+2^y>=2√(2^x*2^y)2^x*2^y=2^(x+y)=2^(y²+y)=2^[(y+1/2)²-1/4]>=2^(-1/4)所以2^x+2^y>=2√[2^(-1/4)]=2*2^(-1/2)=2^(1/2)所以log2(2^x+2^y)>=log2[2^(1/2)]=1/2所以结论不对