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