Question

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Answer 1

$2*2 ^{x}+32*2 ^{-x}>20$
Пусть $2^{x}$=а, тогда
$2a+ 32* a^{-1}>20$
$2a+ frac{32}{a} >20$
$frac{2a ^{2}+32 }{a}-20>0$
$frac{2a ^{2}-20a+32 }{a}>0$
$frac{2(a ^{2}-10a+16) }{a}>0$
D=10²-4*16=36=6²
a₁=(10+6)/2=8
a₂=(10-6)/2=2
a∈(0; 2)∨(8; +∞)
$2^{x}$∈(0; 2)∨(8; +∞), а значит
x∈(-∞;1)∨(3;+∞)