2) 7 х (2х-1) + 5 х (3х +2) = 32
14х - 7 + 15х + 10 = 32
29х = 32- 10 +7
29х = 29
х = 29 : 29
х = 1
1.а)х=-9 х=5
+ _ +
_________________________
-9 5
х∈(-≈;-9)U (5;≈)
б)x=3 x=-6
+ _ +
_________________________
-6 3
x∈(-6;3)
2.a) x(x-7)(x+7)=0⇒x=0,x=7,x=-7
б)2x²+6-17+3x-16=0
2x²+3x-27=0
D=9+216=225 √D=15 x1=(-3-15)/4=-4,5 x2=(-3+15)/4=3
в) х²=а
а²-17а+16=0 а1+а2=17 и а1*а2=16
а1=16⇒х²=16⇒х=4 и х=-4
а2=1⇒х²=1⇒х=1 и х=-1
3)D=t²-100<0
(t-10)(t+10)<0
t=10 t=-10
+ _ +
_______________________
-10 10
t∈(-10;10)
4)5x-2x²≥0
x(5-2x)≥0
x=0 x=2,5
_ + -
__________________________
0 2,5
x∈[0;2,5]
г
(1-2sin²(x/2))²=cos²x
2tg^4(x/2)/(1+tg²(x/2))=2sin^4(x/2)/cos^4(x/2):1/cos^4(x/2)=2sin^4(x/2)=
=2*(1-cosx)²/4=(1-2cosx+cos²x)/2
Получаем
cos²x-(1-2cosx+cos²x)/2=√3/2
2cos²x-1+2cosx-cos²x=√3
cos²x+2cosx-(1+√3)=0
cosx=a
a²+2a-(1+√3)=0
D=4+4+4√3=8+4√3=4(2+√3)
a1=(-2-2√*2+√3)/2=-1-√(2+√3)⇒cosx=-1-√(2+√3)<-1
нет решения
a2=-1+√(2+√3)⇒cosx=-1+√(2+√3)⇒x=+-arccos(√(2+√3)-1)+2πn,n∈z
ж
(1+cos2x)/2+(1+cos4x)/2+(1+cos6x)/2+(1+cos8x)/2=2
4+(cos2x+cos8x)+(cos4x+cos6x)=4
2cos5xcos3x+2cos5xcosx=0
2cos5x(cos3x+cosx)=0
4cos5xcos2xcosx=0
cos5x=0⇒5x=π/2+πn,n∈z⇒x=π/10+πn/5,n∈z
cos2x=0⇒2x=π/2+πk,k∈z⇒x=π/4+πk/2,k∈z
cosx=0⇒x=π/2+πm,m∈z
д
1/2*(cos5x+cos8x)=1/2*(cos2x+cos9x)
cos5x=cos2x
cos5x-cos2x=0
2sin(3x/2)*sin(7x/2)=0
sin(3x/2)=0⇒3x/2=πn⇒x=2πn/3,n∈z
sin(7x/2)=0⇒7x/2=πk,k∈z⇒x=2πk/7,k∈z
Решение уравнений 4 степени сложное.
Способ решения уравнения четвертой степени.
<span>x</span>⁴<span> + Ax</span>³<span> + Bx</span>²<span> + Ex + D = 0 (1)
</span><span>Уравнение (1) можно представить в виде:
(x</span>²<span> + ax + d)(x</span>²<span> + bx + g) = (2)
= x</span>⁴<span> + (a + b)x</span>³<span> + (ab + d + g)x</span>²<span> + (ag + bd)x + dg = 0 (3)
</span>Могу дать только ответы для подтверждения этой мысли:
<span>Ответ:
Корни полинома
x</span>⁴<span><span> + 3</span>x</span>³<span><span> − </span>x</span>²<span><span><span> − 5</span>x<span> − 2</span><span> = 0</span>
равны:
</span><span><span>x1<span> ≈ −2.81360670471645 </span></span><span>P(x1) ≈ 0 </span><span><span>iter = </span>1
</span></span><span><span>x2<span> ≈ −0.999998260217034 = -1 </span></span><span>P(x2) ≈ 0 </span><span><span>iter = </span>4
</span></span><span><span>x3<span> ≈ −0.529318308685604 </span></span><span>P(x3) ≈ 0 </span><span><span>iter = </span>4
</span></span><span><span>x4<span> ≈ 1.34292327361909 </span></span><span>P(x4) ≈ 0 </span><span><span>iter = </span>1</span></span></span>