Đáp án+Giải thích các bước giải:
`a)`
`f(x)=0\tox^2+4x-5=0`
`\tox^2+5x-x-5=0`
`\to(x^2+5x)-(x+5)=0`
`\tox(x+5)-(x+5)=0`
`\to(x-1)(x+5)=0`
`\to` \(\left[ \begin{array}{l}x-1=0\\x+5=0\end{array} \right.\) `\to` \(\left[ \begin{array}{l}x=1\\x=-5\end{array} \right.\)
Vậy `x\in{-5;1}`
`b)`
`g(x)=0\to3x^2-1/2x=0`
`\tox(3x-1/2)=0`
`\to` \(\left[ \begin{array}{l}x=0\\3x-\dfrac{1}{2}=0\end{array} \right.\) `\to`\(\left[ \begin{array}{l}x=0\\x=\dfrac{1}{6}\end{array} \right.\)
Vậy `x\in{1/6;0}`
`c)`
`h(x)=0\tox^2+x-6=0`
`->x^2+6x-x-6=0`
`->(x^2+6x)-(x+6)=0`
`->x(x+6)-(x+6)=0`
`->(x-1)(x+6)=0`
`->` \(\left[ \begin{array}{l}x-1=0\\x+6=0\end{array} \right.\) `\to`\(\left[ \begin{array}{l}x=1\\x=-6\end{array} \right.\)
Vậy `x\in{-6;1}`
`d)`
`r(x)=0\to7x^2-6x-1=0`
`\to7x^2-7x+x-1=0`
`->7x(x-1)+(x-1)=0`
`->(7x+1)(x-1)=0`
`->` \(\left[ \begin{array}{l}7x+1=0\\x-1=0\end{array} \right.\) `->` \(\left[ \begin{array}{l}x=-\dfrac{1}{7}\\x=1\end{array} \right.\)
Vậy `x\in{-1/7;1}`
`e)`
`M(x)=0->x^2+2x+5=0`
Ta có `x^2>=0\tox^2+2x+5>0`
Vậy `M(x)` vô nghiệm
