d=b2-b1=7-9=7+(-9)=-2
bn=b1+d(n-1)
b18=9+(-2)(18-1)=9+(-2)*17=9+(-34)=-25
sn=(b1+bn)n/2
s18=(9+(-25))*18/2=-16*9=-144
2х^2-5х-3=0
д=25-4×2×(-3)=25+24=49
х1=(5-7)/2×2=-1/2=-0.5
х2=(5+7)/2×2=3
3-(-0.5)=3.5см это расстояние
1)=15(√6-1)/(√6+1)(√6-1) +4(√6+2)/(√6-2)(√6+2) - 12(3+√6)/(3-√6)(3+√6)=
=15(√6-1)/(6-1)+4(√6+2)/(6-4) - 12(3+√6)/(9-6)=3(√6-1)+2(√6+2) -4(3+√6)=
=3√6-3+2√6+4-12-4√6=√6-11
2)(√6-11)*(√6+11)=6-121=-115
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)