* * * a³ -b³ =(a-b)(a²+ab+b²) , <span>(a+b)</span>³<span>=a</span>³<span>+3a</span>²<span>b+3ab</span>²<span>+b</span>³ * * *
1) (x+1)³ -(x-1)³ =x(6x+2) ;
(x+1 -(x-1))((x+1)² +(x+1)(x-1) +(x-1)²)=6x²+2x ;
2(3x²+1)=6x²+2x ;
x=1 .
2)(x+2)³-(x-1)³=9x²+36 ;
(x+2 -(x-1))((x+2)² +(x+2)(x-1) +(x-1)²)=9x²+36 ;
3(3x²+3x+3) =9x²+36 ;
9x²+9x+9 =9x²+36;
x=3.
3) (x-2)³-3x²-4=(x-3)³ ;
(x-2)³ -(x-3)³ =3x²+4 ;
(x-2 -(x-3))((x-2)² +(x-2)(x-3) +(x-3)²) = 3x²+4 ;
3x² -15x+19 = 3x²+4 ;
-15x =4-19;
x=1.
4) (x+3)³=x²<span>(x+9) ;
x</span>³ +3x²*3+3x*3²+3³ =x³ +9x² ;
x³ +9x²+27x +27=x³ +9x² ;
27x +27= 0 ;
27x = -27 ;
x= -1 .
Ответ: 4) a^2 - ab - 3a - 3b =
a(a-b) - 3(a-b)
(a-b)(a-3)
9) 5ax - 6bx - 5ay +6by =
5a(x-y) - 6b(x - y) =
(x-y)(5a-6b)
Объяснение:
<span>1) f(x)=sinx-cosx </span>
<span><span>f'(x)=(sinx)' - (cosx)' = cosx - (-sinx) = cosx + sinx </span></span>
<span><span><span>2) f(x)=tgx-4ctgx</span></span></span>
<span>3) f(x)=4x-sinx </span>
<span>f'(x)=(4x)' - (sinx)' = 4 - cosx</span>
<span> <span>4) f(x)=6cosx-1,2x</span></span>
<span><span><span>f'(x)=(6cosx)' - (1,2x)' = -6sinx-1.2</span></span></span>
