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1) (-25)*(45-100)+25*45=25*(100-45+45)=25*100=2500
2) 83*(-98-1)+98*83=83*(-98-1+98)=-83
3) (-15)*(-7+15)-7*15=15(7-15-7)=-15*15=-225
1
сtg3x-ctgx=0
sin(3x-x)/sin3x*sinx=0
sin2x=0 U sin3x*sinx≠0
2x=πn⇒x=πn/2,n∈z U x≠πk,k∈z U x≠πm/3,m∈z
x=πn/2,n∈z U n≠2m/3,m∈z
3
sin(2x+4x)/cos2xcos4x=sin(5x+x)/cos5xcosx
sin6x/cos2xcos4x-sin6x/cos5xcosx=0
sin6x(cos5xcosx-cos2xcos4x)/cosxcos2xcos4xcos5x=0
cosxcos2xcos4xcos5x≠0
sin6x=0⇒x=πn/6,n∈z
cos5xcosx-cos2xcos4x=0
1/2*cos4x+1/2*cos6x-1/2*cos2x-1/2*cos6x=0
1/2*cos4x-1/2*cos2x=0
-1/2*2sinxsin3x=0
sinx=0⇒x=πk,k∈z
sin3x=0⇒x=πm/3,m∈z
X6=x3-125
x6-x3=-125
x3=-125
x=-5
3) ab +a +ab+b = (a+1)(b+1) ab=?
ab +a +ab+b = ab +b +a +1
ab = 1
4) 5t² -4t = 0
t(5t -4) = 0
t = 0 или 5t -4 = 0
5t = 4
t = 0,8
6*) (5x -2)(2x +1) = (5x -2)(4x -1)
10x² -4x +5x -2 = 20x² -8x -5x +2
10x²-14x +4 = 0
5x² -7x +2 = 0
D = b² -4ac = 49 -4*5*2 = 9
x = (7 +-3)/10
x₁ = 1, x₂= 0,4
6) (3x³ +4x²)/x² = 3x +4
4x²/2x = 2x
3x +4 -2x = x +4 = -4 +4 = 0
9) (x³ +mx² +6x -3)(x +1) = x⁴ +mx³ +6x² -3x + x³ +mx² +6x -3=
=x⁴ +(m+1)x³ +(m+6)x² +3x -3
Чтобы слагаемого с "х³" не было, надо, чтобы m+1 = 0, ⇒ m = -1