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\(P\left(x\right)=5^6-6.5^5+6.5^4-6.5^3+6.5^2-6.5+1=5^6-6\left(5^5-5^4-5^3-5^2-5\right)+1=1556\)
\(x^3-6x^2+5x=0\Leftrightarrow x\left(x^2-6x+5\right)=0\)
\(\Leftrightarrow x\left(x^2-x-5x+5\right)=0\)
\(\Leftrightarrow x\left[x\left(x-1\right)-5\left(x-1\right)\right]=0\Leftrightarrow x\left(x-1\right)\left(x-5\right)=0\Leftrightarrow x=0;x=1;x=5\)
\(x^3-6x^2+5x=0\)
\(\Leftrightarrow x.\left(x^2-6x+5\right)=0\)
\(\Leftrightarrow x.\left(x^2-x-5x+5\right)=0\)
\(\Leftrightarrow x.\left[\left(x^2-x\right)-\left(5x-5\right)\right]=0\)
\(\Leftrightarrow x.\left[x\left(x-1\right)-5\left(x-1\right)\right]=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x-5=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=5\end{matrix}\right.\)
Vậy \(x\in\left\{0;1;5\right\}\)
\(âP\left(x\right)=13x^3+4x^2-11x-2\)
\(b.Q\left(x\right)=x^3+9x-5\)
\(c.A\left(x\right)=14x^3-x^2+10x+14\)
\(d.B\left(x\right)=2x^2+x+3\)
a: \(A=-5x^3+9x^3-2x^2-2x^2+x-x+1\)
\(=4x^3-4x^2+1\)
\(B=-4x^3+2x^3-2x^2+2x^2+6x-9x-2\)
\(=-2x^3-3x-2\)
\(C=x^3-6x^2+2x-4\)
b: \(A\left(x\right)+B\left(x\right)-C\left(x\right)\)
\(=4x^3-4x^2+1-2x^3-3x-2+x^3-6x^2+2x-4\)
\(=3x^3-10x^2-x-4\)
\(\dfrac{6x^2-2x+1}{x-1}\)
\(=\dfrac{6x^2-6x+4x-4+5}{x-1}=6x+4+\dfrac{5}{x-1}\)
=> 6x ( x - 1) = 0
=> \(\left[{}\begin{matrix}6x=0\\x-1=0\end{matrix}\right.=>\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
Vậy x = 0 hoặc x = 1