1: ĐKXĐ: x<>-1
\(\left\{{}\begin{matrix}\dfrac{30}{x+1}-4\left|y-1\right|=22\\\dfrac{9}{x+1}+6\left|y-1\right|=21\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{90}{x+1}-12\left|y-1\right|=66\\\dfrac{18}{x+1}+12\left|y-1\right|=42\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{108}{x+1}=108\\\dfrac{9}{x+1}+6\left|y-1\right|=21\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+1=1\\6\left|y-1\right|=21-9=12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=0\\\left|y-1\right|=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=0\\y-1\in\left\{2;-2\right\}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y\in\left\{3;-1\right\}\end{matrix}\right.\)(nhận)
2:
a: Phương trình hoành độ giao điểm là:
\(x^2=5x-m-1\)
=>\(x^2-5x+m+1=0\)
\(\text{Δ}=\left(-5\right)^2-4\cdot1\left(m+1\right)=25-4m-4=-4m+21\)
Để (d) cắt (P) tại hai điểm phân biệt thì Δ>0
=>-4m+21>0
=>-4m>-21
=>\(m< \dfrac{21}{4}\)
