Bài 1:
a) \(A=\left[-2\left(m+1\right)\right]^2-4\left(m-4\right)\)
\(A=\left(-2\right)^2\left(m+1\right)^2-4m+16\)
\(A=4\left(m^2+2m+1\right)-4m+16\)
\(A=4m^2+8m+4-4m+16\)
\(A=4m^2+4m+20\)
\(A=\left(2m\right)^2+2.m.2+4+16\)
\(A=\left(2m+2\right)^2+16\)
Vì \(\left(2m+2\right)^2\ge0\) với mọi m
\(\Rightarrow\left(2m+2\right)^2+16\ge16\)
Mà \(16>0\)
\(\Rightarrow\left(2m+2\right)^2+16>0\)
\(\Rightarrow\left[-2\left(m+1\right)\right]^2-4\left(m-4\right)>0\) ( Đpcm )
b) \(B=\left[-\left(m+2\right)\right]^2-4.2m\)
\(B=\left(-1\right)^2\left(m+2\right)^2-8m\)
\(B=m^2+2m.2+4-8m\)
\(B=m^2+4m+4-8m\)
\(B=m^2-4m+4\)
\(B=m^2-2.m.2+2^2\)
\(B=\left(m-2\right)^2\)
Vì \(\left(m-2\right)^2\ge0\) với mọi m
\(\Rightarrow\left[-\left(m+2\right)\right]^2-4.2m\ge0\) ( Đpcm )
c) \(C=\left(m+1\right)^2-4.2.\left[-\left(m+3\right)\right]\)
\(C=m^2+2m+1-8\left(-m-3\right)\)
\(C=m^2+2m+1+8m+24\)
\(C=m^2+10m+25\)
\(C=\left(m+5\right)^2\)
Vì \(\left(m+5\right)^2\ge0\) với mọi m
\(\Rightarrow\left(m+1\right)^2-4.2\left[-\left(m+3\right)\right]\ge0\) ( Đpcm )
