Question

1) Tìm x biết 

a) x³-5x²+x-5=0

b) x⁴-2x^3+10x²-20x=0

2) tìm cặp a,b thỏa mãn a-b=ab-1

Answer 1

1)

a) \(x^3-5x^2+x-5=0\Rightarrow x^2.\left(x-5\right)+\left(x-5\right)\)

\(\Rightarrow\left(x^2+1\right).\left(x-5\right)=0\Rightarrow\orbr{\begin{cases}x^2+1=0\\x-5=0\end{cases}\Rightarrow}\orbr{\begin{cases}x^2=-1\left(sai\right)\\x=5\end{cases}}\)\(KL:x=5\)

b) \(x^4-2x^3+10x^2-20x=0\Rightarrow x^3.\left(x-2\right)+10x\left(x-2\right)\)

\(\Rightarrow\left(x-2\right).\left(x^3+10x\right)\Rightarrow\orbr{\begin{cases}x-2=0\\x^3+10x=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=2\\x\left(x^2+10\right)=0\Rightarrow x=0\end{cases}}\)

Vì nếu x² + 10 = 0 => x² = -10 ( sai )

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