a) 4.5x+2 - 5x+1 = 475
b) 4x+3 - 14 . 4x = 200
c) x47y chia het cho 2;3 va chia 5 du 2
d) 4x7y chi het cho 2;3;5;9
giup mik vs mik dang can gap, toan lop 6 nha
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Thực hiện phép chia đơn thức ta có :
4x3 + 11x2 + 5x + 5 : x + 2 dư 7
Để 4x3 + 11x2 + 5x + 5 ⋮ x + 2 thì 7 ⋮ x + 2
=> x + 2 ∈ Ư(7) = { 1; 7; -1; -7 }
Ta có bảng:
x+2 | 1 | 7 | -1 | -7 |
x | -1 | 5 | -3 | -9 |
Vậy để 4x3 + 11x2 + 5x + 5 ⋮ x + 2 thì 7 ⋮ x + 2 thì x ∈ { -9; -3; -1; 5 }
a, \(4\left(18-5x\right)-12\left(3x-7\right)=15\left(2x-16\right)-6\left(x+14\right)\)
\(\Leftrightarrow72-20x-36x+84=30x-240-6x-84\)
\(\Leftrightarrow156-56x=24x-324\)
\(\Leftrightarrow-80x+480=0\Leftrightarrow x=-6\)
b, \(5\left(3x+5\right)-4\left(2x-3\right)=5x+3\left(2x-12\right)+1\)
\(\Leftrightarrow15x+25-8x+12=5x+6x-36+1\)
\(\Leftrightarrow7x+37=11x-35\)
\(\Leftrightarrow-4x+72=0\Leftrightarrow x=18\)
c, \(2\left(5x-8\right)-3\left(4x-5\right)=4\left(3x-4\right)+11\)
\(\Leftrightarrow10x-16-12x+15=12x-16+11\)
\(\Leftrightarrow-2x-1=12x-5\)
\(\Leftrightarrow-14x+4=0\Leftrightarrow x=\frac{2}{7}\)
d, \(5x-3\left\{4x-2\left[4x-3\left(5x-2\right)\right]\right\}=182\)
\(\Leftrightarrow5x-3\left[4x-15x+6\right]=182\)
\(\Leftrightarrow5x-3\left(-11x+6\right)=182\)
\(\Leftrightarrow5x+33x-18-182=0\)
\(\Leftrightarrow38x-200=0\Leftrightarrow x=\frac{100}{19}\)
a, \(4\left(18-5x\right)-12\left(3x-7\right)=15\left(2x-16\right)-6\left(x+14\right)\)
\(\Rightarrow72-20x-36x+84=30x-240-6x-84\)
\(\Rightarrow-20x-36x-30x+6x=-240-84-72-84\)
\(\Rightarrow-80x=-480\Rightarrow x=6\)
b, \(5\left(3x+5\right)-4\left(2x-3\right)=5x+3\left(2x+12\right)+1\)
\(\Rightarrow15x+25-8x+12=5x+6x+36+1\)
\(\Rightarrow15x-8x-5x-6x=36+1-25-12\)
\(\Rightarrow-4x=0\Rightarrow x=0\)
c, \(2\left(5x-8\right)-3\left(4x-5\right)=4\left(3x-4\right)+11\)
\(\Rightarrow10x-16-12x+15=12x-16+11\)
\(\Rightarrow10x-12x-12x=-16+11+16-15\)
\(\Rightarrow-14x=-4\Rightarrow x=\dfrac{2}{7}\)
d, \(5x-3\left\{4x-2\left[4x-3\left(5x-2\right)\right]\right\}=182\)
\(\Rightarrow5x-3\left[4x-2\left(4x-15x+6\right)\right]=182\)
\(\Rightarrow5x-3\left(4x-8x+30x-12\right)=182\)
\(\Rightarrow5x-12x+24x-90x+36=182\)
\(\Rightarrow-73x=182-36\)
\(\Rightarrow-73x=146\Rightarrow x=-2\)
Chúc bạn học tốt!!!
Bài 13 :
Câu a : Ta có :
\(\left(3x+2\right)^2-49\)
\(=\left(3x+2\right)^2-7^2\)
\(=\left(3x+2-7\right)\left(3x+2+7\right)\)
\(=\left(3x-5\right)\left(3x+9\right)\)
\(=3\left(3x-5\right)\left(x+3\right)\)
Vì 3 chia hết cho 3 nên \(3\left(3x-5\right)\left(x+3\right)\) chia hết cho 3 .
\(\Rightarrow\left(3x+2\right)^2-49\) chia hết cho 3 ( đpcm )
Câu b : Ta có :
\(x\left(4x-1\right)^2-81x\)
\(=x\left[\left(4x-1\right)^2-9^2\right]\)
\(=x\left(4x-1-9\right)\left(4x-1+9\right)\)
\(=x\left(4x-10\right)\left(4x+8\right)\)
\(=8x\left(2x-5\right)\left(x+2\right)\)
Vì 8 chia hết cho 8 nên \(8x\left(2x-5\right)\left(x+2\right)\) chia hết cho 8
\(\Rightarrow x\left(4x-1\right)^2-81x\) chia hết cho 8 ( đpcm )
Bài 14 :
Câu a : \(x^2+3x+2=\left(x+1\right)\left(x+2\right)\)
Câu b : \(x^2+x+6\) ( Không phân tích được )
Câu c : \(x^2-5x+6=\left(x-2\right)\left(x-3\right)\)
Câu d : \(x^2+5x-6=\left(x-1\right)\left(x+6\right)\)
Câu e : \(x^2+4x+3=\left(x+1\right)\left(x+3\right)\)
Câu f : \(x^2-5x+4=\left(x-1\right)\left(x-4\right)\)
\(a,4.5^{x+2}-5^{x+1}=475\)
\(4.5^x.5^2-5^x.5=475\)
\(5^x.100-5^x.5=475\)
\(5^x\left(100-5\right)=475\)
\(5^x.95=475\)
\(5^x=5\)
\(\Rightarrow x=1\)
\(b,4^{x+3}-14.4^x=200\)
\(4^x.4^3-14.4^x=200\)
\(4^x.64-14.4^x=200\)
\(4^x\left(64-14\right)=200\)
\(4^x.50=200\)
\(4^x=4^1\)
\(\Rightarrow x=1\)