Đáp án:
`a) `\(\left[ \begin{array}{l}x=-1\\x=5\end{array} \right.\)
`b)` \(\left[ \begin{array}{l}x=-3\\x=5\\x=2\end{array} \right.\)
`c)`\(\left[ \begin{array}{l}x=3\\x=-4\end{array} \right.\)
Giải thích các bước giải:
`a) x^3-9x^2+15x+25=0`
`<=> x^3+x^2-10x^2-10x+25x+25=0`
`<=> x^2(x+1)-10x(x+1)+25(x+1)=0`
`<=> (x+1)(x^2-10x+25)=0`
`<=> (x+1)(x-5)^2=0`
`<=>`\(\left[ \begin{array}{l}x+1=0\\x-5=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-1\\x=5\end{array} \right.\)
`b) x^3-4x^2-11x+30=0`
`<=> x^3+3x^2-7x^2-21x+10x+30=0`
`<=> x^2(x+3)-7x(x+3)+10(x+3)=0`
`<=>(x+3)(x^2-7x+10)=0`
`<=> (x+3)(x^2-5x-2x+10)=0`
`<=> (x+3)(x-5)(x-2)=0`
`<=>`\(\left[ \begin{array}{l} x+3=0\\x-5=0\\x-2=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-3\\x=5\\x=2\end{array} \right.\)
`c) 2x^4+x^3-22x^2+15x-36=0`
`<=> 2x^4-6x^3+7x^3-21x^2-x^2+3x+12x-36=0`
`<=> 2x^3(x-3)+7x^2(x-3)-x(x-3)+12(x-3)=0`
`<=> (x-3)(2x^3+7x^2-x+12)=0`
`<=> (x-3)(2x^3+8x^2-x^2-4x+3x+12)=0`
`<=> (x-3)(x+4)(2x^2-x+3)=0`
Do `2x^2-x+3=2(x^2-1/2x+3/2)=2(x^2-2x. 1/4+1/16+23/16)`
`=2(x-1/4)^2+23/8>=23/8>0` với mọi `x`
`=>`\(\left[ \begin{array}{l}x-3=0\\x+4=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=3\\x=-4\end{array} \right.\)
