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a. x2 - 11 = \(x^2-\left(\sqrt{11}\right)^2=\left(x-\sqrt{11}\right)\left(x+\sqrt{11}\right)\)
b. x2 - 5 = \(x^2-\left(\sqrt{5}\right)^2=\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)\)
c. x2 - 7 = \(x^2-\left(\sqrt{7}\right)^2=\left(x+\sqrt{7}\right)\left(x-\sqrt{7}\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\left(x^2-6x+9\right)-2=\left(x-3\right)^2-\sqrt{2^2}=\left(x-3-\sqrt{2}\right)\left(x-3+\sqrt{2}\right)\)
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\(x+7\sqrt{x}+10=\left(\sqrt{x}+2\right)\left(\sqrt{x}+5\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^2-x-1=x^2-x+\frac{1}{4}-\frac{5}{4}=\left(x-\frac{1}{2}\right)^2-\left(\frac{\sqrt{5}}{2}\right)^2=\left(x-\frac{1-\sqrt{5}}{2}\right)\left(x-\frac{1+\sqrt{5}}{2}\right)\)
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A=x14+x7+1
=(x14+x13+x12)-(x13+x12+x11)+(x11+x10+x9)-(x10+x9+x8)+(x8+x7+x6)-(x6+x5+x4)+(x5+x4+x3)-(x3+x2+x)+(x2+x+1)
Đặt B=x2+x+1
=>A=x12B-x11B+x9B-x8B+x6B-x4B+x3B-xB+B
=>A=B(x12-x11+x9-x8+x6-x4+x3-x+1)
Thay B=x2+x+1 vào A là xong
![](https://rs.olm.vn/images/avt/0.png?1311)