phân tích đa x64+x32+1 thành nhân tử
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13 tháng 7 2016
a) \(x^3\left(x^2-7\right)^2-36x=x\left[\left(x^3-7x\right)^2-6^2\right]\)
\(=x\left(x^3-7x-6\right)\left(x^3-7x+6\right)\)
\(x\left[\left(x-3\right)\left(x+1\right)\left(x+2\right)\right].\left[\left(x+3\right)\left(x-2\right)\left(x-1\right)\right]\)
\(=\left(x-3\right)\left(x-2\right)\left(x-1\right).x.\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
b) Không pt được.
c) Không pt được.
LD
2
22 tháng 12 2018
Ta có:
x^4 + 64 = (x²)² + 8² + 2x².8 - 2.x².8
= (x² + 8)² - (4x)²
= (x² - 4x + 8)(x² + 4x + 8)
22 tháng 12 2018
Ta có:
x^4 + 64 = (x²)² + 8² + 2x².8 - 2.x².8
= (x² + 8)² - (4x)²
= (x² - 4x + 8)(x² + 4x + 8)
TH
2
18 tháng 10 2015
x4 + 64 = (x4 + 16x2 + 64) - 16x2 = (x2 + 8)2 - (4x)2 = (x2 - 4x + 8).(x2 + 4x + 8)
22 tháng 4 2018
Ta có
x4 + 64
= (x4 + 16x2 + 64) - 16x2
= (x2 + 8)2 - (4x)2
= (x2 - 4x + 8).(x2 + 4x + 8)
hok tốt
27 tháng 7 2017
Ta có:
x^4 + 64 = (x²)² + 8² + 2x².8 - 2.x².8
= (x² + 8)² - (4x)²
= (x² - 4x + 8)(x² + 4x + 8)
k nhoa
27 tháng 7 2017
Ta có:
x^4 + 64 = (x²)² + 8² + 2x².8 - 2.x².8
= (x² + 8)² - (4x)²
= (x² - 4x + 8)(x² + 4x + 8)
k nhoa
NH
1
25 tháng 9 2021
1) \(64-y^2=8^2-y^2=\left(8-y\right)\left(8+y\right)\)
2) \(81-x^2=9^2-x^2=\left(9-x\right)\left(9+x\right)\)
3) \(100-a^2=10^2-a^2=\left(10-a\right)\left(10+a\right)\)
4) \(144-b^2=12^2-b^2=\left(12-b\right)\left(12+b\right)\)
KQ
4
24 tháng 9 2018
\(x^4+64\)
\(=\left(x^2\right)^2+8^2+2x^2.8-2x^2.8\)
\(=\left(x^2+8\right)^2-\left(4x^2\right)\)
\(=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\)
TN
28 tháng 10 2017
x^4+4=x^4 + 4x^2 +4 - 4x^2=(x^2)^2+ 2.x^2.2+2^2 - (2x)^2 = (x^2+2)-(2x)^2 =(x^2+2-2x)(2^2+2-2x)
28 tháng 10 2017
\(x^4+4=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)
\(x^{64}+x^{32}+1\\ =x^{64}+2x^{32}+1+x^{32}-2x^{32}\\ =\left[\left(x^{32}\right)^2+2\cdot x^{32}\cdot1+1^2\right]-x^{32}\\ =\left(x^{32}+1\right)^2-\left(x^{16}\right)^2\\ =\left(x^{32}-x^{16}+1\right)\left(x^{32}+x^{16}+1\right)\\ =\left(x^{32}-x^{16}+1\right)\left[\left(x^{32}+2x^{16}+1\right)+x^{16}-2x^{16}\right]\\ =\left(x^{32}-x^{16}+1\right)\left[\left(x^{16}+1\right)^2-x^{16}\right]\\ =\left(x^{32}-x^{16}+1\right)\left(x^{16}-x^8+1\right)\left(x^{16}+x^8+1\right)\\ =\left(x^{32}-x^{16}+1\right)\left(x^{16}-x^8+1\right)\left[\left(x^{16}+2x^8+1\right)-x^8\right]\\ =\left(x^{32}-x^{16}+1\right)\left(x^{16}-x^8+1\right)\left[\left(x^8+1\right)^2-x^8\right]\\ =\left(x^{32}-x^{16}+1\right)\left(x^{16}-x^8+1\right)\left(x^8-x^4+1\right)\left(x^8+x^4+1\right)\\ =\left(x^{32}-x^{16}+1\right)\left(x^{16}-x^8+1\right)\left(x^8-x^4+1\right)\left[\left(x^8+2x^4+1\right)-x^4\right]\\ =\left(x^{32}-x^{16}+1\right)\left(x^{16}-x^8+1\right)\left(x^8-x^4+1\right)\left[\left(x^4+1\right)^2-x^4\right]\\ =\left(x^{32}-x^{16}+1\right)\left(x^{16}-x^8+1\right)\left(x^8-x^4+1\right)\left(x^4-x^2+1\right)\left(x^4+x^2+1\right)\)
\(=\left(x^{32}-x^{16}+1\right)\left(x^{16}-x^8+1\right)\left(x^8-x^4+1\right)\left(x^4-x^2+1\right)\left[\left(x^4+2x^2+1\right)-x^2\right]\\ =\left(x^{32}-x^{16}+1\right)\left(x^{16}-x^8+1\right)\left(x^8-x^4+1\right)\left(x^4-x^2+1\right)\left[\left(x^2+1\right)^2-x^2\right]\\ =\left(x^{32}-x^{16}+1\right)\left(x^{16}-x^8+1\right)\left(x^8-x^4+1\right)\left(x^4-x^2+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\)
\(x^{64}+x^{32}+1\)
\(=x^{64}+2x^{32}-x^{32}+1\)
\(=\left(x^{64}+2^{32}+1\right)-x^{32}\)
\(=\left(x^{32}+1\right)^2-\left(x^{16}\right)^2\)
\(=\left(x^{32}+1-x^{16}\right)\left(x^{32}+1+x^{16}\right)\)