\(C=\dfrac{\left|x+5\right|+\left|7-x\right|+8}{\left|x+5\right|+\left|x-7\right|+3}\)
\(C=\dfrac{\left|x+5\right|+\left|7-x\right|+8}{\left|x+5\right|+\left|7-x\right|+3}\)
Đặt:
\(A=\left|x+5\right|+\left|7-x\right|\)
Áp dụng bđt:
\(\left|a\right|+\left|b\right|\ge\left|a+b\right|\)
\(A\ge\left|x+5+7-x\right|\)
\(A\ge12\)
Dấu "=" xảy ra khi:
\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x+5\ge0\Rightarrow x\ge-5\\7-x\ge0\Rightarrow x\le7\end{matrix}\right.\\\left\{{}\begin{matrix}x+5< 0\Rightarrow x< -5\\7-x< 0\Rightarrow x>7\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow-5\le x\le7\)
\(C\le\dfrac{12+8}{12+3}\)
\(C\le\dfrac{20}{15}\)
\(C\le\dfrac{4}{3}\)
Dấu "=" xảy ra khi:
\(-5\le x\le12\)
