a.
Do vế trái không âm \(\Rightarrow\) vế phải không âm \(\Rightarrow x\ge0\)
\(\Rightarrow\left\{{}\begin{matrix}x+1>0\\x+2>0\\....\\x+100>0\end{matrix}\right.\)
Phương trình trở thành:
\(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=101x\)
\(\Leftrightarrow100x+1+2+...+100=101x\)
\(\Leftrightarrow x=1+2+...+100=\dfrac{100.101}{2}=5050\)
b.
\(f\left(2\right)=4a+2b+c\)
\(f\left(-1\right)=a-b+c\)
\(\Rightarrow f\left(2\right)+f\left(-1\right)=5a+b+2c=0\)
\(\Rightarrow f\left(-1\right)=-f\left(2\right)\)
\(\Rightarrow f\left(2\right).f\left(-1\right)=f\left(2\right).\left[-f\left(2\right)\right]=-\left[f\left(2\right)\right]^2\le0\) (đpcm)
