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1) D(y)=R или (-∞; +∞)
2) 6x²+x-1≥0
D=1+24=25
x₁=(-1-5)/12=-6/12=-1/2
x₂=(-1+5)/12=4/12=1/3
+ - +
-------- -1/2 ------------ 1/3 -------------
\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\
D(y)=(-∞; -1/2]U[1/3; +∞)
3) 2x²+3x-5>0
D=9+40=49
x₁=(-3-7)/4=-2.5
x₂=(-3+7)/4=1
+ - +
-------- -2.5 ------------ 1 ---------------
\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\
D(y)=(-∞; -2.5)U(1; +∞)
4) 3x-5x²≥0
5x²-3x≤0
5x(x-3/5)≤0
x(x-0.6)≤0
x=0 x=0.6
+ - +
----------- 0 ----------- 0.6 ------------
\\\\\\\\\\\\\
D(y)=[0; 0.6]
5) 3x²+5x-2≠0
D=25+24=49
x₁≠(-5-7)/6≠ -2
x₂≠(-5+7)/6=2/6≠1/3
D(y)=(-∞; -2)U(-2; 1/3)U(1/3; +∞)
6) 1) x-7≠0
x≠7
2)
(11+x)(x-7)≥0
(x+11)(x-7)≥0
x= -11 x=7
+ - +
-------- -11 ----------- 7 -------------
\\\\\\\\\\ \\\\\\\\\\\\\\\
D(y)=(-∞; -11]U(7; +∞)
7) (64-x)(x+2)(3x-x²)≥0
-(x-64)(x+2)*(-(x²-3x))≥0
(x-64)(x+2)(x²-3x)≥0
x(x-64)(x+2)(x-3)≥0
x=0 x=64 x=-2 x=3
+ - + - +
-------- -2 ---------- 0 --------- 3 ------------ 64 ----------
\\\\\\\\\\ \\\\\\\\\\\\ \\\\\\\\\\\\
D(y)=(-∞; -2]U[0; 3]U[64; +∞)
2) 6x²+x-1≥0
D=1+24=25
x₁=(-1-5)/12=-6/12=-1/2
x₂=(-1+5)/12=4/12=1/3
+ - +
-------- -1/2 ------------ 1/3 -------------
\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\
D(y)=(-∞; -1/2]U[1/3; +∞)
3) 2x²+3x-5>0
D=9+40=49
x₁=(-3-7)/4=-2.5
x₂=(-3+7)/4=1
+ - +
-------- -2.5 ------------ 1 ---------------
\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\
D(y)=(-∞; -2.5)U(1; +∞)
4) 3x-5x²≥0
5x²-3x≤0
5x(x-3/5)≤0
x(x-0.6)≤0
x=0 x=0.6
+ - +
----------- 0 ----------- 0.6 ------------
\\\\\\\\\\\\\
D(y)=[0; 0.6]
5) 3x²+5x-2≠0
D=25+24=49
x₁≠(-5-7)/6≠ -2
x₂≠(-5+7)/6=2/6≠1/3
D(y)=(-∞; -2)U(-2; 1/3)U(1/3; +∞)
6) 1) x-7≠0
x≠7
2)
(11+x)(x-7)≥0
(x+11)(x-7)≥0
x= -11 x=7
+ - +
-------- -11 ----------- 7 -------------
\\\\\\\\\\ \\\\\\\\\\\\\\\
D(y)=(-∞; -11]U(7; +∞)
7) (64-x)(x+2)(3x-x²)≥0
-(x-64)(x+2)*(-(x²-3x))≥0
(x-64)(x+2)(x²-3x)≥0
x(x-64)(x+2)(x-3)≥0
x=0 x=64 x=-2 x=3
+ - + - +
-------- -2 ---------- 0 --------- 3 ------------ 64 ----------
\\\\\\\\\\ \\\\\\\\\\\\ \\\\\\\\\\\\
D(y)=(-∞; -2]U[0; 3]U[64; +∞)