3х³-х²+18х-6=0
<span>(3х³-х²)+(18х-6)=0
</span>х²(3х-1)+6(3х-1)=0
(3х-1)(х²+6)=0
3х-1=0 или х²+6=0
зх=1 х²=-6
х=1/3 нет корней
Ответ: 1/3
4*(-9)*2-3*(-9)*2-3*2+6
-36*2-27*2-6+6
-72-54-6+6
-126
Cos²4x+sin²2x-1=0
(cos(2*2x))²+sin²2x-1=0
(1-2sin²2x)²+sin²2x-1=0
1-4sin²2x+4sin⁴2x+sin²2x-1=0
4sin⁴2x-3sin²2x=0
sin²2x*(4sin²2x-3)=0
sin²2x=0 или 4sin²2x-3=0
1. sin²2x=0, sin2x=0. 2x=πn, n∈Z. x=πn/2, n∈Z
2. 4sin²2x-3=0, sin²2x=3/4. sin2x=+-√(3/4). sin2x=+-√3/2
a. sin2x=-√3/2
n∈Z
n∈Z
n∈Z
b. sin2x=√3/2
n∈z
ответ:
n∈Z
1) <u> x³ (x-1)⁴ (x+5) </u> <0
(1-4x)(x+3)² (x-8)
{1-4x≠0
{x+3≠0
{x-8≠0
{x≠1/4
{x=-3
{x=8
<u> x³ (x-1)⁴ (x+5) </u> <0
-4(x-1/4)(x+3)² (x-8)
<u> x³(x-1)⁴ (x+5) </u>>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) <u>(x²+4x+3) (4x²-4x+1)</u> ≤0
x²-11x+30
Разложим на множители:
x²+4x+3=0
D=16-12=4
x₁=<u>-4-2</u>=-3
2
x₂=<u>-4+2</u>=-1
2
x²+4x+3=(x+3)(x+1)
4x²-4x+1=(2x-1)²
x²-11x+30=0
D=121-120=1
x₁=<u>11-1</u>=5
2
x₂=<u>11+1</u>=6
2
x²-11x+30=(x-5)(x-6)
<u>(x+3)(x+1)(2x-1)²</u> ≤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)
