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b, A=[(a+1)(a+7)][(a+3)(a+5)]+15
=>A=(a2+8a+7)(a2+8a+15)+15
Đặt a2+8a+11= t
=>a2+8a+7= t-4 và a2+8a+15= t+4
=>A=(t-4)(t+4)+15
=>A=t2-16+15
=t2-1=(t-1)(t+1)
Thay t = a2+8a+11
=>A=(a2+8a+11-1)(a2+8a+11+1)
=>A=(a2+8a+10)(a2+8a+12)
a) \(x^2+2xy+7x+7y+y^2+10\)
\(=\left(x+y\right)^2+7\left(x+y\right)+\frac{49}{4}-\frac{9}{4}\)
\(=\left(x+y+\frac{7}{2}\right)^2-\frac{9}{4}\)
\(=\left(x+y+\frac{7}{2}-\frac{3}{2}\right)\left(x+y+\frac{7}{2}+\frac{3}{2}\right)\)
\(=\left(x+y-2\right)\left(x+y+5\right)\)
Bài 1:
a) \(M=x^2+x+1\)
\(=x^2+2.x.\frac{1}{2}+\frac{1}{4}-\frac{1}{4}+1\)
\(=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\)
Vì \(\left(x+\frac{1}{2}\right)^2\ge0;\forall x\)
\(\Rightarrow\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\ge0+\frac{3}{4};\forall x\)
Hay \(M\ge\frac{3}{4};\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x+\frac{1}{2}=0\)
\(\Leftrightarrow x=\frac{-1}{2}\)
Vậy \(MIN\)\(M=\frac{3}{4}\)\(\Leftrightarrow x=\frac{-1}{2}\)
b) \(N=3-2x-x^2\)
\(=-x^2-2x+3\)
\(=-\left(x^2+2x+1\right)+4\)
\(=-\left(x+1\right)^2+4\)
Vì \(-\left(x+1\right)^2\le0;\forall x\)
\(\Rightarrow-\left(x+1\right)^2+4\le0+4;\forall x\)
Hay \(N\le4;\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x+1=0\)
\(\Leftrightarrow x=-1\)
Vậy MAX \(N=4\)\(\Leftrightarrow x=-1\)
Bài 2:
Vì a chia 3 dư 1 nên a có dạng \(3k+1\left(k\in N\right)\)
Vì b chia 3 dư 2 nên b có dạng \(3t+2\left(t\in N\right)\)
Ta có: \(ab=\left(3k+1\right)\left(3t+2\right)\)
\(=\left(3k+1\right).3t+\left(3k+1\right).2\)
\(=9kt+3t+6k+2\)
\(=3.\left(3kt+t+2k\right)+2\)chia 3 dư 2 .
\(\)
1a) Ta có: M = x2 + x + 1 = (x2 + x + 1/4) + 3/4 = (x + 1/2)2 + 3/4
Ta luôn có: (x + 1/2)2 \(\ge\)0 \(\forall\)x
=> (x + 1/2)2 + 3/4 \(\ge\)3/4 \(\forall\)x
Dấu "=" xảy ra khi : x + 1/2 = 0 <=> x = -1/2
Vậy Mmin = 3/4 tại x = -1/2
b) Ta có: N = 3 - 2x - x2 = -(x2 + 2x + 1) + 4 = -(x + 1)2 + 4
Ta luôn có: -(x + 1)2 \(\le\)0 \(\forall\)x
=> -(x + 1)2 + 4 \(\le\)4 \(\forall\)x
Dấu "=" xảy ra khi : x + 1 = 0 <=> x = -1
Vậy Nmax = 4 tại x = -1
2019x2+x=2020y2+y (1)
=> (x-y)[2019(x+y)+1]=0
Xét 2019(x+y)+1=0=> đpcm
Xét x-y=0=> x=y, thay vào (1) ta được x=y=0
=> 2019(x+y)+1=1=> đpcm
\(a,6x^2-9x=3x\left(x-3\right)\)
\(b,x^3-2x^2-3x+6\)
\(=\left(x^3-2x^2\right)-\left(3x-6\right)\)
\(=x^2\left(x-2\right)-3\left(x-2\right)\)
\(=\left(x^2-3\right)\left(x-2\right)\)
\(e,2x\left(x-y\right)-3y\left(x-y\right)\)
\(=\left(2x-3y\right)\left(x-y\right)\)
a) 6x2 - 9x
= 3x (2x - 3)
b) x3 - 2x2 - 3x + 6
= x2(x - 2) - 3 (x - 2)
=(x - 2) (x2 - 3)
c) x2 - 4x + 4 - 9y2
= (x - 2)2 - 9y2
=(x - 2 - 3y)(x - 2 + 3y)
e) 2x(x - y) - 3y(x - y)
= (x - y)(2x - 3y)
xin lỗi mình học ngu nên không biết làm nhìu nha
Bài 2
\(a,x^3+2x^2+x\)
\(=x.\left(x^2+2x+1\right)\)
\(b,xy+y^2-x-y\)
\(=y.\left(x+y\right)-\left(x+y\right)\)
\(=\left(y-1\right).\left(x+y\right)\)
bài 3
\(a,3x.\left(x^2-4\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x=0\\x^2=4\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=2,x=-2\end{cases}}\)
vậy x=0,x=2 hay x=-2
\(b,xy+y^2-x-y=0\)
\(y.\left(x+y\right)-\left(x+y\right)=0\)
\(\left(y-1\right).\left(x+y\right)=0\)
\(\Rightarrow\orbr{\begin{cases}y-1=0\\x+y=0\end{cases}\Rightarrow\orbr{\begin{cases}y=1\\x=-1\end{cases}}}\)
vậy x=-1, y=1
\(a,\left(x-2\right).\left(x-3\right)-\left(x+3\right).\left(x-3\right)\)
\(=\left(x-3\right).\left(x-2-x+3\right)=x-3\)
\(b,\frac{\left(x^2+4x+4\right)}{x+2}-4x+5=\frac{\left(x+2\right)^2}{x+2}-4x+5\)
\(x+2-4x+5=-3x+7\)
a) \(\left(x-2\right)\left(x-3\right)-\left(x+3\right)\left(x-3\right)\)
\(=\left(x^2-5x+6\right)-\left(x^2-9\right)\)
\(=x^2-5x+6-x^2+9\)
\(=15-5x\)
b) \(\left(x^2+4x+4\right):\left(x+2\right)-\left(4x-5\right)\)
\(=\left(x+2\right)^2:\left(x+2\right)-\left(4x-5\right)\)
\(=\left(x+2\right)-4x+5\)
\(=x+2-4x+5\)
\(=7-3x\)