cos(4x-6x) + cos 2x= cos2x+cos2x=2cos2x=2(cos^2(x)- sin^2(x)).
1.a)(1/3)ˣ=9;⇒
3⁻ˣ=3²;
-x=2;⇒x=-2;
б)2²ˣ⁻⁷=8;
2²ˣ⁻⁷=2³;
2x-7=3;
2x=10;x=5;
в)log₂x=3;
x=2³=8;
г)log¹/₂(3x+1)=-2;(3x+1)>0;x>-1/3;
(1/2)⁻²=(3x+1);
3x+1=4;
3x=3;x=1;
2.а)3ˣ⁺¹ -3ˣ=18;
3·3ˣ-3ˣ=18;
2·3ˣ=18;
3ˣ=18/2=9=3²;
x=2;
б)log₂x+log₄x=6;
log₂x+1/2·log₂x=6;
3/2log₂x=6;
log₂x=6:(3/2)=4;
x=2⁴=16;
в)log₁/₃(log₃x)=-1;
-log₃(log₃x)=-1;
log₃(log₃x)=1;
log₃x=3;
x=3³=27;
Приложение.
x=2 y=-2
x=-4 y=-8
X^3 - 7x^2 + 16x - 12 = 0
Сгруппируем
x^3 - 3x^2 - 4x^2 + 12x + 4x - 12 = 0
x^2 (x - 3) - 4x (x - 3) + 4(x - 3) = 0
(x - 3) (x^2 - 4x + 4) = 0
(x - 3) (x - 2)^2 = 0
x - 3 = 0
x = 3
(x - 2)^2 = 0
x - 2 = 0
x = 2
Ответ
2 ; 3
cosy*<span>√</span>(sinx)=0 (1)