Mọi người giúp e bài 11 6 câu đầu với ạ.
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NV
Nguyễn Việt Lâm
Giáo viên
17 tháng 9 2021
\(A=x^7-4x^3+x^2+2=x^3\left(x^4-4\right)+x^2+2\)
\(=x^3\left(x^2-2\right)\left(x^2+2\right)+x^2+2\)
\(=\left(x^2+2\right)\left(x^3\left(x^2-2\right)+1\right)\)
\(=\left(x^2+2\right)\left(x^5-2x^3+1\right)\)
\(=\left(x^2+2\right)\left(x^5-x^4+x^4-x^3-x^3+x^2-x^2+x-x+1\right)\)
\(=\left(x^2+2\right)\left[x^4\left(x-1\right)+x^3\left(x-1\right)-x^2\left(x-1\right)-x\left(x-1\right)-\left(x-1\right)\right]\)
\(=\left(x^2+2\right)\left(x-1\right)\left(x^4+x^3-x^2-x-1\right)\)
NV
Nguyễn Việt Lâm
Giáo viên
6 tháng 10 2021
\(x^6+x^4-3x^2-4x+6\)
\(=\left(x^6+2x^5+4x^4+6x^3+5x^2\right)-\left(2x^5+4x^4+8x^3+12x^2+10x\right)+\left(x^4+2x^3+4x^2+6x+5\right)+1\)
\(=x^2\left(x^4+2x^3+4x^2+6x+5\right)-2x\left(x^4+2x^3+4x^2+6x+5\right)+\left(x^4+2x^3+4x^2+6x+5\right)+1\)
\(=\left(x^4+2x^3+4x^2+6x+5\right)\left(x^2-2x+1\right)+1\)
\(=\left[\left(x^4+2x^3+x^2\right)+3\left(x^2+2x+1\right)+2\right]\left(x-1\right)^2+1\)
\(=\left[\left(x^2+x\right)^2+3\left(x+1\right)^2+2\right]\left(x-1\right)^2+1\ge1\)
Dấu "=" xảy ra khi \(x=1\)
NV
Nguyễn Việt Lâm
Giáo viên
6 tháng 10 2021
\(=ab\left(a-b\right)\left(a+b\right)+c^3\left(a-b\right)-c\left(a^3-b^3\right)\)
\(=\left(a-b\right)\left(a^2b+ab^2\right)+c^3\left(a-b\right)-\left(a-b\right)\left(a^2c+abc+b^2c\right)\)
\(=\left(a-b\right)\left(a^2b+ab^2+c^3-a^2c-abc-b^2c\right)\)
\(=\left(a-b\right)\left[ab\left(a-c\right)+b^2\left(a-c\right)-c\left(a^2-c^2\right)\right]\)
\(=\left(a-b\right)\left[ab\left(a-c\right)+b^2\left(a-c\right)-\left(a-c\right)\left(ac+c^2\right)\right]\)
\(=\left(a-b\right)\left(a-c\right)\left(ab+b^2-ac-c^2\right)\)
\(=\left(a-b\right)\left(a-c\right)\left[a\left(b-c\right)+\left(b-c\right)\left(b+c\right)\right]\)
\(=\left(a-b\right)\left(b-c\right)\left(a-c\right)\left(a+b+c\right)\)
CC
3
HY
3
1: Ta có: \(A=25x^4-24x^2-1\)
\(=25x^4-25x^2+x^2-1\)
\(=\left(x^2-1\right)\left(25x^2+1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(25x^2+1\right)\)
2: Ta có: \(A=64x^4+63x^2-1\)
\(=64x^4+64x^2-x^2-1\)
\(=\left(x^2+1\right)\left(64x^2-1\right)\)
\(=\left(x^2+1\right)\left(8x-1\right)\left(8x+1\right)\)
3: Ta có: \(A=x^4-15x^2+50\)
\(=x^4-5x^2-10x^2+50\)
\(=\left(x^2-5\right)\left(x^2-10\right)\)
4: Ta có: \(A=-10x^4+9x^2+1\)
\(=-10x^4+10x^2-x^2+1\)
\(=\left(x^2-1\right)\left(-10x^2-1\right)\)
\(=-\left(10x^2+1\right)\left(x-1\right)\left(x+1\right)\)