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1) x2 -7x + 10 = x2 - 2x - 5x + 10 = x(x - 2) - 5(x - 2) = (x - 5)(x - 2)
2) x2 + 3x + 2 = x2 + 2x + x + 2 = x(x + 2) + (x + 2) = (x + 1)(x + 2)
3) x2 - 7x + 12 = x2 - 3x - 4x + 12 = x(x - 3) - 4(x - 3) = (x - 3)(x - 4)
4) x2 + 7x + 12 = x2 + 3x + 4x + 12 = x(x + 3) + 4(x + 3) = (x + 3)(x + 4)
5) 16x - 5x2 - 3 = 15x - 5x2 + x - 3 = -5x(x - 3) + (x - 3) = (x - 3)(1 - 5x)
6) 6x2 + 7x - 3 = 6x2 - 2x + 9x - 3 = 2x(3x - 1) + 3(3x - 1) = (2x + 3)(3x - 1)
7) 3x2 - 3x - 6 = 3x2 - 6x + 3x - 6 = 3x(x - 2) + 3(x - 2) = (x - 2)(3x + 3) = 3(x - 2)(x + 1)
8) 3x2 + 3x - 6 = 3x2 - 3x + 6x - 6 = 3x(x - 1) + 6(x - 1) = (x - 1)(3x + 6) = 3(x - 1)(x + 2)
9) 6x2 - 13x + 6 = 6x2 - 9x - 4x + 6 = 3x(2x - 3) - 2(2x - 3) = (3x - 2)(2x - 3)
10) 6x2 + 15x + 6 = 6x2 + 12x + 3x + 6 = 6x(x + 2) + 3(x + 2) = (x + 2)(6x + 3) = 3(x + 2)(3x + 1)
11) 6x2 - 20x + 6 = 6x2 - 18x - 2x + 6 = 6x(x -3) - 2(x - 3) = (6x - 2)(x - 3) = 2(3x - 1)(x - 3)
12) 8x2 + 5x - 3 = 8x2 + 8x - 3x - 3 = 8x(x + 1) - 3(x + 1) = (x + 1)(8x - 3)
\(a,\left(x-3\right)^2-x\left(x-4\right)=5\\ \Rightarrow x^2-6x+9-x^2+4x=5\\ \Rightarrow-2x=-4\\ \Rightarrow x=2\\ b,x\left(x-6\right)+2x-12=0\\ \Rightarrow x\left(x-6\right)+2\left(x-6\right)=0\\ \Rightarrow\left(x+2\right)\left(x-6\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-2\\x=6\end{matrix}\right.\)
f: =>\(\dfrac{14}{3\left(x-4\right)}-\dfrac{x+2}{x-4}=\dfrac{-3}{2\left(x-4\right)}-\dfrac{5}{6}\)
=>28-6(x+2)=-9-5(x-4)
=>28-6x-12=-9-5x+20
=>-6x+16=-5x+11
=>-x=-5
=>x=5
d: =>\(\dfrac{12x+1}{11x-4}=\dfrac{20x+17-20x+8}{18}=\dfrac{25}{18}\)
=>25(11x-4)=18(12x+1)
=>275x-100=216x+18
=>59x=118
=>x=2
f: =>\(\dfrac{14}{3\left(x-4\right)}-\dfrac{x+2}{x-4}=\dfrac{-3}{2\left(x-4\right)}-\dfrac{5}{6}\)
=>28-6(x+2)=-9-5(x-4)
=>28-6x-12=-9-5x+20
=>-6x+16=-5x+11
=>-x=-5
=>x=5
tìm x thỏa mãn điều kiện :
a) (x+12)2 - 92 = 0
b) 20x3-132+7x = 45x2-38x
c) 8x3+12x2+6x+7-3(2x+1)2 = 6
Ta có : (x + 12)2 - 92 = 0
<=> (x + 12)2 = 92
=> (x + 12)2 = 81
\(\Leftrightarrow\orbr{\begin{cases}\left(x+12\right)^2=9^2\\\left(x+12\right)^2=\left(-9\right)^2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x+12=9\\x+12=-9\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-3\\x=-21\end{cases}}\)
tìm x thỏa mãn điều kiện :
a) (x+12)2 - 92 = 0
b) 20x3-152+7x = 45x2-38x
c) 8x3+12x2+6x+7-3(2x+1)2 = 6
x + 20736 = 20 730
x = 20730 - 20736 = -6
\(3x^{12}+20x^6+6=???????\)Câu b đề là gì bạn?
Câu a:
x + 124 = 20730
x = 20730 - 124
x = - 6