Bài 1:
\(M=\frac{13}{27-\left(x-2\right)^2}\)
Có: \(\left(x-2\right)^2\ge0\)
\(\Rightarrow27-\left(x-2\right)^2\ge27\)
\(\Rightarrow\frac{13}{27-\left(x-2\right)^2}\ge\frac{13}{27}\)
\(\Rightarrow M\ge\frac{13}{27}\)
Vậy GTNN của \(M=\frac{13}{27}\)
Dấu "=" xảy ra khi: \(\left(x-2\right)^2=0\\ \left(x-2\right)^2=0^2\\ \Rightarrow x-2=0\\ x=0+2\\ x=2\)
Bài 2:
\(P=\frac{29}{15+\left(x+5\right)^2}\)
Có: \(\left(x+5\right)^2\ge0\)
\(\Rightarrow15+\left(x+5\right)^2\ge15\\ \Rightarrow\frac{29}{15+\left(x+5\right)^2}\ge\frac{29}{15}\\ \Rightarrow P\ge\frac{29}{15}\)
Vậy GTLN của \(P=\frac{29}{15}\)
Dấu "=" xảy ra khi: \(\left(x+5\right)^2=0\\ \left(x+5\right)^2=0^2\\ \Rightarrow x+5=0\\ x=0-5\\ x=-5\)
