Question

若实数xy满足4^x+4^y=2^(x+1)+2^(y+1)则s=2^x+2^y的取值范围

Answer 1

题设条件可化为(2^x-1)²+(2^y-1)²=2.故可设2^x-1=(√2)cost,2^y-1=(√2)sint.===>2^x=1+(√2)cost>0,2^y=1+(√2)sint>0.===>sint,cost＞-√2/2.===>0≤ts=2^x+2^y=2+2sin[t+(π/4)].===>s=2+2sin[t+(π/4)].显然2