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\(x^3-x^2-x-2=x^3-2x^2+x^2-2x+x-2\) \(-2\)
\(=\) \(x^2\left(x-2\right)+x\left(x-2\right)+\left(x-2\right)\)
\(=\left(x^2+x+1\right)\left(x-2\right)\)
\(x^3-6x^2-x+30=x^3+2x^2-8x^2-16x+15x+30\)
\(=x^2\left(x+2\right)-8x\left(x+2\right)+15\left(x+2\right)\)
\(=\) \(\left(x^2-8x+15\right)\left(x+2\right)\)
\(=\left(x^2-5x-3x+15\right)\left(x+2\right)\)
\(=\left(x-5\right)\left(x-3\right)\left(x+2\right)\)
\(x^3-3x^2+3x-1\) =0
=>\(\left(x-1\right)^3\)=0
=>x-1=0
=>x=1
vậy x =1
\(x^3-3x^2+3x-1=0\)
\(\Leftrightarrow\left(x-1\right)^3\)
\(\Leftrightarrow x-1=0\)
\(\Leftrightarrow x=1\)
chắc bn nảy hỏi lun cả bài tâp về nhà quá, làm km 1 câu
a) = a+a+a + a +a +1 -a -a -a = a(a+a+1) +(a+a+1) - a(a+a+1)= (a+a+1)(a-a+1)
tự bn thêm mũ 4;3;2 vào được là bn làm dc cac câu sau
a,\(-4x^2+4x-1\)
\(\Leftrightarrow\left(-2x-1\right)^2\)
b,\(\left(2x+1\right)^2-4\left(x-1\right)^2\)
\(\Rightarrow\left[2x+1-2\left(x-1\right)\right].\left[2x+1+2\left(x-1\right)\right]\)
\(\Rightarrow\left(2x+1-2x+2\right)\left(2x+1+2x-2\right)\)
\(\Rightarrow3\left(4x-1\right)\)
c,\(\left(2x-y\right)^2-4x^2+12x-9\)
\(\Leftrightarrow\left(2x+y\right)^2-\left(4x^2-12x+9\right)\)
\(\Leftrightarrow\left(2x+y\right)^2-\left(2x-3\right)^2\)
\(\Leftrightarrow\left(2x+y-2x+3\right)\left(2x+y+2x-3\right)\)
\(\Rightarrow\left(y+3\right)\left(4x+y-3\right)\)
d,\(\left(x+1\right)^2-4\left(x+1\right)y^2+4y^4\)
\(\Leftrightarrow\left(x+1\right)^2-2\left(x+1\right)2y^2+2^2y^4\)
\(\Leftrightarrow\left(x+1\right)^2-2\left(x+1\right)2y^2+4\left(y^2\right)^2\)
\(\Leftrightarrow\left(x+1\right)^2-2\left(x+1\right)-2y^2+\left(2y^2\right)^2\)
\(\Leftrightarrow\left(x+1-2y^2\right)^2\)
Ta có : x3 + 2x2 + 2x + 1
= x3 + x2 + (x2 + 2x + 1)
= x2(x + 1) + (x + 1)2
= (x + 1) ( x2 + x + 1)
a)\(\left(ab-1\right)^2+\left(a+b\right)^2=a^2b^2-2ab+1+a^2+2ab+b^2\)
\(=a^2b^2+a^2+b^2+1\)
\(=a^2\left(b^2+1\right)+\left(b^2+1\right)\)
\(\left(a^2+1\right)\left(b^2+1\right)\)
b)\(x^3+2x^2+2x+1=x^3+x^2+x^2+x+x+1\)
\(=x^2\left(x+1\right)+x\left(x+1\right)+x+1\)
\(=\left(x^2+x+1\right)\left(x+1\right)\)
1/ \(x^2+2xy+y^2-x-y-12=\left(x+y\right)^2+6\left(x+y\right)+9-7\left(x+y\right)-21\)
\(=\left(x+y+3\right)^2-7\left(x+y+3\right)=\left(x+y+3\right)\left(x+y-4\right)\)
2/ \(4x^4-32x^2+1=\left(4x^4+4x^2+1\right)-36x^2\)
\(=\left(2x^2+1\right)^2-36x^2=\left(2x^2-6x+1\right)\left(2x^2+6x+1\right)\)
3/ \(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2=2x^4-2x^3-2x+2\)
\(=2\left(x-1\right)^2\left(x^2+x+1\right)\)
Còn lại tự làm nhé
i don't now
mong thông cảm !
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