2的x次方加2的y次方等于一,求x加y取值范围,咋算尼?不等式

Question

2的x次方加2的y次方等于一,求x加y取值范围,咋算尼?不等式

Answer 1

1=2^x+2^y 

≥2√(2^x×2^y)

=2×√2^(x+y)

=2¹×2^[(x+y)/2]

=2^[(x+y)/2+1]

即2^[(x+y)/2+1]≤1=2º

∴(x+y)/2+1≤0

(x+y)/2≤-1

∴x+y≤-2

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