1. (1) --- x≥0 ; (2) --- x = -3 ∅
2. (1) --- x²-3x+2≠0 ≡ (x-1)(x-2)≠0 ≡ x≠1 ; x≠2
(2) --- x=1 ; x=2 ∅
3. (1) --- x(x²-3x+2) = 0 (2) ⇒ (1)
4. (1) --- x≠1 ; (2) --- x=1 ∅
5. (1) --- x≠1 ; (2) --- x=1 ∅
6. (1) --- (2) ⇒ (1)
7. ⇔
8. ⇔
9. (1) ⇒ (2)
10. ⇔
11. (1) ⇒ (2)
12. (1) ⇒ (2)
7
(cos²a/sin²a-cos²a):(sin²a/cos²a-sin²a)=
=cos²a*(1-sin²a)/sin²a :sin²a(1-cos²a)/cos²a=
=cos²a*cos²a/sin²a *cos²a/sin²a*sin²a=cos^6a/sin^6a=ctg^6a
8
{(x+y)/(x-y)+(x-y)/(x+y)=5/2
{x²+y²=20
(x+y)/(x-y)=a
a+1/a=5/2
2a²-5a+2=0,a≠0
D=25-16=9
a1=(5-3)/4=1/2⇒(x+y)/(x-y)=1/2
2x+2y=x-y
2x-x=-y-2y
x=-3y
подставим во 2 уравнение
y²+9y²=20
10y²=20
y²=2
y1=-√2,x1=3√2
y2=√2,x2=-3√2
a2=(5+3)/4=2⇒⇒(x+y)/(x-y)=2
x+y=2x-2y
y+2y=2x-x
x=3y
подставим во 2 уравнение
9y²+y²=20
10y²=20
y²=2
y1=-√2,x1=-3√2
y2=√2,x2=3√2
Ответ (3√2;-√2),(-3√2;√2),(-3√2;-√2),(3√2;√2)
<span>p(a)=p1(a)+p2(a), если:
p1(a)=9−8a; p2(a)=−5−9a
р(а)=9-8а+(-5-9а)=-5-9а+9-8а=4-17а
p1(a)=−3−5a; p2(a)=8−9a
р(а)=-3-5а+8-9а=5-14а
p(a)=3x^6 +7x+2; p(a)=x^6+x−6
р(а)=</span>3x^6 +7x+2+x^6+x−6=4х^6+8х-4
<span>
p(a)=x^10+x^7 −4; p (a)=2x^10 +2x^7+3
р(а)=</span>x^10+x^7−4+2x^10+2x^7+3=3х^10+3х^7-1