Tìm a, b thuộc Z biết:
a) (a - 7).(b + 3)
b) (ab - 2).(b + 5)
c) (a.15).(b + 8)
d) (ab - 1).(b + 7)
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a, (a-2)(b+3) = 5
ta có 5= 5 x1 = 1 x 5
=> ta xét 2 TH
TH1 a-2 = 1 => a= 3
và b+ 3 = 5 => b = 2
TH2 bn tự xét nhé
ta có
(ab - 5a ) + ( 3b - 15 ) = 7
=> a( b-5) + 3(b-5) = 7
=> (a+3)(b-5) = 7
ta có 7=1 x 7 = 7 x1
=> ta xét 2TH
TH1 a + 3 = 1 => a= -2
b-5 = 7 => b= 12
TH2 bn tự xét nhé
Bài 1 : Bài giải
Ta có :
\(A=7+7^2+7^3+...+7^8\)
\(A=\left(7+7^2+7^3+7^4\right)+\left(7^5+7^6+7^7+7^8\right)\)
\(A=7\left(1+7+7^2+7^3\right)+7^4\left(1+7+7^2+7^3\right)\)
\(A=7\cdot400+7^4\cdot400\)
\(A=7\cdot8\cdot50+7^4\cdot8\cdot50\)
\(A=50\left(7\cdot8+7^4\cdot8\right)\text{ }⋮\text{ }50\)
Bài 1 : Bài giải
Ta có :
\(A=7+7^2+7^3+...+7^8\)
\(A=\left(7+7^2+7^3+7^4\right)+\left(7^5+7^6+7^7+7^8\right)\)
\(A=7\left(1+7+7^2+7^3\right)+7^4\left(1+7+7^2+7^3\right)\)
\(A=7\cdot400+7^4\cdot400\)
\(A=7\cdot8\cdot50+7^4\cdot8\cdot50\)
\(A=50\left(7\cdot8+7^4\cdot8\right)\text{ }⋮\text{ }50\)
CÂU 10:
a, -x - 84 + 214 = -16 b, 2x -15 = 40 - ( 3x +10 )
x = - ( -16 -214 + 84 ) 2x + 3x = 40 -10 +15
x = 16 + 214 - 84 5x = 45
x = 146 x = 9
c, \(|-x-2|-5=3\) d, ( x - 2)(2x + 1) = 0
\(|-x-2|=8\) => x - 2 = 0 hoặc 2x + 1 = 0
=> - x - 2 = 8 hoặc x + 2 = 8 \(\orbr{\begin{cases}x-2=0\\2x+1=0\end{cases}=>}\orbr{\begin{cases}x=2\\x=-\frac{1}{2}\end{cases}}\)
\(\orbr{\begin{cases}-x-2=8\\x+2=8\end{cases}=>\orbr{\begin{cases}x=-10\\x=6\end{cases}}}\)
\(1,=\left(a+b\right)^3-3ab\left(a+b\right)+c^3-3abc\\ =\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2\right)-3ab\left(a+b+c\right)\\ =\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)\\ 2,=a^{10}-a+a^5-a^2+a^2+a+1\\ =a\left(a^3-1\right)\left(a^3+1\right)+a^2\left(a^3-1\right)+\left(a^2+a+1\right)\\ =\left(a-1\right)\left(a^2+a+1\right)\left(a^4+a^2+a\right)+\left(a^2+a+1\right)\\ =\left(a^2+a+1\right)\left[\left(a-1\right)\left(a^4+a^2+a\right)+1\right]\\ =\left(a^2+a+1\right)\left(a^5-a^4+a^3-a+1\right)\)
\(3,=a^8+a^7-a^7+a^6-a^6+a^5-a^5+a^4-a^4+a^3-a^3+a^2-a^2+a+1\\ =a^6\left(a^2+a+1\right)-a^5\left(a^2+a+1\right)+a^3\left(a^2+a+1\right)-a^2\left(a^2+a+1\right)+\left(a^2+a+1\right)\\ =\left(a^2+a+1\right)\left(a^6-a^5+a^3-a^2+1\right)\)
\(4,=a^8+a^7-a^6+a^6+1=a^6\left(a^2+a+1\right)-\left(a^3-1\right)\left(a^3+1\right)\\ =\left(a^2+a+1\right)\left[a^6-\left(a-1\right)\left(a^3+1\right)\right]\\ =\left(a^2+a+1\right)\left(a^6-a^4-a+a^3-1\right)\)
\(5,=\left(a^{16}+2a^8b^8+b^{16}\right)-a^8b^8=\left(a^4+b^4\right)^2-\left(a^4b^4\right)^2\\ =\left(a^4+b^4-a^4b^4\right)\left(a^4+b^4+a^4b^4\right)\\ 6,=\left(a^2+8a+7\right)\left(a^2+8a+15\right)+15\\ =\left(a^2+8a+11\right)^2-16+15\\ =\left(a^2+8a+11\right)^2-1\\ =\left(a^2+8a+10\right)\left(a^2+8a+12\right)\)
Câu 7 mình làm riêng nhé
\(7,=8x^3y^2+4x^2y^3+y^2z^3-y^3z^2+x^2z^2\left(2x+z\right)\\ =\left(8x^3y^2+y^2z^3\right)+\left(4x^2y^3-y^3z^2\right)+x^2z^2\left(2x+z\right)\\ =y^2\left(2x+z\right)\left(4x^2-2xz+z^2\right)+y^3\left(2x-z\right)\left(2x+z\right)+x^2z^2\left(2x+z\right)\\ =\left(2x+z\right)\left(4x^2y^2-2xyz+y^2z^2+2xy^3-2y^3z+x^2z^2\right)\)
Từ đây chịu thôi ;-;