Question

giải phương trình sau :

a) \(x^3-x^2-21x+45=0\)

b) \(2x^3-5x^2+8x-3=0\)

làm giúp mình nha các bạn!!^^

 

Answer 1

a. \(x^3-x^2-21x+45=0\Rightarrow\left(x^3+5x^2\right)-\left(6x^2+30x\right)+\left(9x+45\right)=0\)

\(\Rightarrow x^2\left(x+5\right)-6x\left(x+5\right)+9\left(x+5\right)=0\)

\(\Rightarrow\left(x+5\right)\left(x-3\right)^2=0\Rightarrow\orbr{\begin{cases}x=-5\\x=3\end{cases}}\)

Vậy x=-5 hoặc x=3

b. \(2x^3-5x^2+8x-3=0\Rightarrow\left(2x^3-x^2\right)-\left(4x^2-2x\right)+\left(6x-3\right)=0\)

\(\Rightarrow x^2\left(2x-1\right)-2x\left(2x-1\right)+3\left(2x-1\right)=0\)

\(\Rightarrow\left(2x-1\right)\left(x^2-2x+3\right)=0\Rightarrow2x-1=0\)do \(x^2-2x+3\ne0\forall x\)

\(\Rightarrow x=\frac{1}{2}\)