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a) ( a + b + c ) 2 + ( a + b - c ) 2 -2 x ( a+b) 2
2a+2b+2x+2a+2b-2c-2.(2a+2b)
2a+2b+2c+2a+2b-2c-4a-4b
4a+4b-4a-4b=0
b) 2x.( 2x -1 ) 2 -3x.( x+3 )( x-3) - 4x.(x+1).2
2x.(4x-2)-3x2-9x-3x2+9x-4x(2x+2)
8x2-4x-3x2-9x-3x2+9x-8x2-8x
-12x-3x2
c) ( a-b+c).2 -(b-c).2 + 2ab - 2ac
2a-2b+2c-2b+2c+2ab-2ac
2a-4b+4c+2ab-2ac
d) (3x+1).2 - 2(3x+1)( 3x+5 )+(3x+5).2
6x+2-6x-2-6x-10+6x+10=0
A) \(\left(x-3\right)^2-\left(x+2\right)^2\)
\(=\left(x-3-x-2\right)\left(x-3+x+2\right)\)
\(=-5.\left(2x-1\right)\)
B) \(\left(4x^2+2xy+y^2\right)\left(2x-y\right)-\left(2x+y\right)\left(4x^2-2xy+y^2\right)\)
\(=\left(2x\right)^3-y^3-\left[\left(2x\right)^3+y^3\right]\)
\(=8x^3-y^3-8x^3-y^3\)
\(=-2y^3\)
C) \(x^2+6x+8\)
\(=x^2+6x+9-1\)
\(=\left(x+3\right)^2-1\)
\(=\left(x+3-1\right)\left(x+3+1\right)\)
\(=\left(x+2\right)\left(x+4\right)\)
bài 3 A) \(x^2-16=0\)
\(\left(x-4\right)\left(x+4\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-4=0\\x+4=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=4\\x=-4\end{cases}}\)
vậy \(\orbr{\begin{cases}x=4\\x=-4\end{cases}}\)
B) \(x^4-2x^3+10x^2-20x=0\)
\(x^3\left(x-2\right)+10x\left(x-2\right)=0\)
\(\left(x^3+10x\right)\left(x-2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^3+10x=0\\x-2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x\left(x^2+10\right)=0\\x=2\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}\)
vậy \(\orbr{\begin{cases}x=0\\x=2\end{cases}}\)
Bài 1 :
x2-2x+2>0 với mọi x
=x2-2.x.1/4+1/16+31/16
=(x-1/4)2 + 31/16
Vì (x-1/4)2 \(\ge\) 0 nên (x-1/4)2 + 31/16 \(\ge\) 0 với mọi x (đfcm)
Bài 1 :
\(A=26^2-24^2=\left(26-24\right)\left(26+24\right)=2.50=100\)
\(B=27^2-25^2=\left(27-25\right)\left(27+25\right)=2.52=104\)
Vì \(100< 104\Rightarrow A< B\)
Bài 2 :
\(4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x-1\right)\left(x+1\right)=11\)
\(\Rightarrow4\left(x^2+2x+1\right)+4x^2-4x+1-8\left(x^2-1\right)=11\)
\(\Rightarrow4x^2+8x+4+4x^2-4x+1-8x^2+8=11\)
\(\Rightarrow4x=-2\)\(\Leftrightarrow x=-\frac{1}{2}\)
Bài 1 :
(a^2+b^2)(x^2+y^2)=(ax+by)^2
<=> a^2x^2 + a^2y^2 + b^2x^2 + b^2y^2 = a^2x^2 + 2abxy + b^2y^2
<=> a^2y^2 + b^2x^2 = 2abxy
<=> a^2y^2 + b^2x^2 - 2abxy = 0
<=> (ay - bx)^2 = 0
=> ay - bx = 0
=> ay = bx
=> a/x = b/y ( x,y khác 0)