Ответы
Ответ дал:
1
1) x³ (x-1)⁴ (x+5) <0
(1-4x)(x+3)² (x-8)
{1-4x≠0
{x+3≠0
{x-8≠0
{x≠1/4
{x=-3
{x=8
x³ (x-1)⁴ (x+5) <0
-4(x-1/4)(x+3)² (x-8)
x³(x-1)⁴ (x+5) >0
(x-1/4)(x+3)² (x-8)
x³(x-1)⁴ (x+5)(x-1/4)(x+3)² (x-8) >0
x=0 x=1 x=-5 x=1/4 x=-3 x=8
+ - - + - - +
-------- -5 --------- -3 --------- 0 --------- 1/4 -------- 1 --------- 8 -----------
\\\\\\\\ \\\\\\\\\\\\ \\\\\\\\\\\\\
x∈(-∞; -5)U(0; 1/4)U(8; +∞)
2) (x²+4x+3) (4x²-4x+1) ≤0
x²-11x+30
Разложим на множители:
x²+4x+3=0
D=16-12=4
x₁=-4-2=-3
2
x₂=-4+2=-1
2
x²+4x+3=(x+3)(x+1)
4x²-4x+1=(2x-1)²
x²-11x+30=0
D=121-120=1
x₁=11-1=5
2
x₂=11+1=6
2
x²-11x+30=(x-5)(x-6)
(x+3)(x+1)(2x-1)² ≤0
(x-5)(x-6)
{x-5≠0
{x-6≠0
{x≠5
{x≠6
(x+3)(x+1)(2x-1)²(x-5)(x-6)≤0
x=-3 x=-1 x=1/2 x=5 x=6
+ - + + - +
-------- -3 ------- -1 ------------ 1/2 ---------- 5 ----------- 6 -------------
\\\\\\\\\ \\\\\\\\\\\\
x∈[-3; -1]U(5; 6)
(1-4x)(x+3)² (x-8)
{1-4x≠0
{x+3≠0
{x-8≠0
{x≠1/4
{x=-3
{x=8
x³ (x-1)⁴ (x+5) <0
-4(x-1/4)(x+3)² (x-8)
x³(x-1)⁴ (x+5) >0
(x-1/4)(x+3)² (x-8)
x³(x-1)⁴ (x+5)(x-1/4)(x+3)² (x-8) >0
x=0 x=1 x=-5 x=1/4 x=-3 x=8
+ - - + - - +
-------- -5 --------- -3 --------- 0 --------- 1/4 -------- 1 --------- 8 -----------
\\\\\\\\ \\\\\\\\\\\\ \\\\\\\\\\\\\
x∈(-∞; -5)U(0; 1/4)U(8; +∞)
2) (x²+4x+3) (4x²-4x+1) ≤0
x²-11x+30
Разложим на множители:
x²+4x+3=0
D=16-12=4
x₁=-4-2=-3
2
x₂=-4+2=-1
2
x²+4x+3=(x+3)(x+1)
4x²-4x+1=(2x-1)²
x²-11x+30=0
D=121-120=1
x₁=11-1=5
2
x₂=11+1=6
2
x²-11x+30=(x-5)(x-6)
(x+3)(x+1)(2x-1)² ≤0
(x-5)(x-6)
{x-5≠0
{x-6≠0
{x≠5
{x≠6
(x+3)(x+1)(2x-1)²(x-5)(x-6)≤0
x=-3 x=-1 x=1/2 x=5 x=6
+ - + + - +
-------- -3 ------- -1 ------------ 1/2 ---------- 5 ----------- 6 -------------
\\\\\\\\\ \\\\\\\\\\\\
x∈[-3; -1]U(5; 6)
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