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1) $2/(5 ^{x+1} -1)+(5 ^{x+1} -2)/(5 ^{x+1} -3) \geq 2$
ОДЗ
$5 ^{x+1} \neq 1;x+1 \neq 0;x \neq -1$
$5 ^{x+1} \neq 2;x+1 \neq log(5)2 ; x \neq -1+log(5)2$
$5 ^{x+1} \neq 3;x+1 \neq log(5)3;x \neq -1+log(5)3$
$5 ^{x+1} =a$
2/(a-1) + (a-2)/(a-3)≥2
(2a-6+a²-2a-a+2)/(a-1)(a-3) -2≥0
(a²-a-4-2a²+8a-6)/(a-1)(a-3)≥0
(a²-7a+10)/(a-1)(a-3)≤0
a1+a2=7 U a1*a2=10⇒a1=2 U a2=5
a=1 U a=3
+ _ + _ +
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1 2 3 5
11<5^(x+1)≤2⇒0<x+1≤log(5)2⇒-1<x≤-1+log(5)2<br>3<5^(x+1)≤5⇒log(5)3<x+1≤1⇒-1+log(5)3<x≤0<br>x∈(-1;-1+log(5)2] U (-1+log(5)3;0]
2)[2/(25x²+40x+7) +(25x²+40x+4)/2]²≥4
(25x²+40x+7)/2=b
(1/b +b)²≥4
(1/b +b -2)(1/b +b -2)≥0
(b²-2b+1)/b *(b²+2b+1)/b≥0
(b-1)²(b+1)²/b²≥0
b<0 U b>0⇒b≠0
25x²+40x+7≠0
D=1600-700=900
x1=(-40-30)/50=-1,4 U x2=(-40+30)/50=-0,2
x∈(-∞;-1,4) U (-1,4;-0.2) U (-0,2;∞)
Ответ x∈(-1;-1+log(5)2] U (-1+log(5)3;-0,2) (-0,2;0]