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\(x^7+x^5+1\)
\(\left(x^2+x+1\right)\left(x^5-x^4+x^3-x+1\right)\)
k cho mình nha
\(3-\sqrt{3}+15-3\sqrt{5}=18-\sqrt{3}-3\sqrt{5}=\sqrt{3}\left(6\sqrt{3}-1-\sqrt{15}\right)\)
= (x^5-2x^4)-(6x^4-12x^3)+(9x^3-18x^2)-(16x^2-32x)+(48x-96)
= (x-2).(x^4-6x^3+9x^2-16x+48)
= (x-2). [ (x^4-3x^3)-(3x^3-9x^2)-(16x-48) ]
= (x-2).(x-3).(x^3-3x^2-16)
= (x-2).(x-3).[ (x^3-4x^2)+(x^2-16) ]
= (x-2).(x-3).(x-4).(x^2+x+4)
k mk nha
\(x^3-ax^2-2x+2a=0\Leftrightarrow x^2\left(x-a\right)-2\left(x-a\right)=0\)
\(\Leftrightarrow\left(x^2-2\right)\left(x-a\right)=0\) \(\Rightarrow\left[{}\begin{matrix}x=\sqrt{2}\\x=-\sqrt{2}\\x=a\end{matrix}\right.\)
Để pt có 3 nghiệm pb \(\Leftrightarrow a\ne\pm\sqrt{2}\)
TH1: \(a=\frac{\sqrt{2}-\sqrt{2}}{2}\Rightarrow a=0\)
TH2: \(\sqrt{2}=\frac{a-\sqrt{2}}{2}\Rightarrow a=3\sqrt{2}\)
TH3: \(-\sqrt{2}=\frac{a+\sqrt{2}}{2}\Rightarrow a=-3\sqrt{2}\)
Vậy \(a=\left\{0;\pm3\sqrt{2}\right\}\)
\(x+\sqrt{x}+2\sqrt{x}+2\)
= \(\sqrt{x}\left(\sqrt{x}+1\right)+2\left(\sqrt{x}+1\right)\)
= \(\left(\sqrt{x}+2\right)\left(\sqrt{x}+1\right)\)
\(2x-2\sqrt{x}+3\sqrt{x}-3\)
= \(2\sqrt{x}\left(\sqrt{x}-1\right)+3\left(\sqrt{x}-1\right)\)
= \(\left(2\sqrt{x}+3\right)\left(\sqrt{x}-1\right)\)
\(a^4-6a^3+27a^2-54a+32\)
\(=\left(a^4-a^3\right)-\left(5a^3-5a^2\right)+\left(22a^2-22a\right)-\left(32a-32\right)\)
\(=\left(a-1\right)\left(a^3-5a^2+22a-32\right)\)