1) (3x²-x-2) √(2x-1) =0
ОДЗ: 2x-1≥0
2x≥1
x≥0.5
3x² -x-2=0 √(2x-1) =0
D=1+4*3*2=25 2x-1=0
x₁=1-5= -4 = -2 (нет) 2x=1
6 6 3 x=0.5
x₂=1+5=1
6
Ответ: 0,5; 1.
3) y=(sinx) - 5
E(y)=[-6; -4]
4) 5 * 7^(log₇ 3) = 5*3=15
5) 2cos(π+x)=1
-2cosx=1
cosx=-1/2
x=+ 2π/3 + 2πn, n∈Z
Ответ: + 2π/3 + 2πn, n∈Z.
7) 3x-10 ≤0
2x+1
2x+1≠0
x≠-0.5
(3x-10)(2x+1)≤0
3*(x-10/3)*2(x+1/2)≤0
(x-10/3)(x+1/2)≤0
x=10/3 x=-1/2
+ - +
-------- -1/2 ----------- 10/3 ---------------
\\\\\\\\\\\\\\\\
x∈(-1/2; 10/3]
б) 16x² -x ≤0
12-x
12-x≠0
x≠12
(16x² -x)(12-x)≤0
-x(16x-1)(x-12)≤0
-16x(x-1/16)(x-12)≤0
x(x-1/16)(x-12)≥0
x=0 x=1/16 x=12
- + - +
------------ 0 ------------ 1/16 ------------- 12 ---------------
\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\
x∈[0; 1/16]U(12; +∞)
9.
а) (2x²-3x-2) √(3x+1) =0
ОДЗ: 3x+1≥0
3x≥-1
x≥-1/3
2x²-3x-2=0 √(3x+1)=0
D=9+4*2*2=25 3x+1=0
x₁=3-5= -2 =-1/2 (нет) 3x=-1
4 4 x=-1/3
x₂=3+5=2
4
Ответ: -1/3; 2.
б) (6x-5) √(2x²-5x+2) =0
ОДЗ: 2x²-5x+2≥0
2x²-5x+2=0
D=25-4*2*2=9
x₁=5-3 = 2/4=1/2
4
x₂=5+3=2
4
+ - +
------------ 1/2 ------------- 2 --------------
\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\
x≤1/2 и x≥2
6x-5=0 √(2x²-5x+2)=0
6x=5 2x²-5x+2=0
x=5/6 (нет) x₁=1/2
x₂=2
Ответ: 1/2; 2.
в) (2x-3) √(3x²-5x-2)=0
ОДЗ: 3x²-5x-2≥0
3x²-5x-2=0
D=25+4*3*2=25+24=49
x₁=5-7=-2/6=-1/3
6
x₂=5+7=2
2
+ - +
-------------- -1/3---------------- 2 ----------------
\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\
x≤-1/3 и x≥2
2x-3=0 √(3x²-5x-2)=0
2x=3 3x²-5x-2=0
x=1.5 (нет) x₁=-1/3
x₂=2
Ответ: -1/3; 2.