18:
a: \(A=4x-x^2+5\)
\(=-x^2+4x-4-1\)
\(=-\left(x-2\right)^2-1\le-1\forall x\)
Dấu '=' xảy ra khi x-2=0
=>x=2
b: \(B=-x^2-4y^2+2x-4y+3\)
\(=-x^2+2x-1-4y^2-4y-1+5\)
\(=-\left(x-1\right)^2-\left(2y+1\right)^2+5\le5\forall x,y\)
Dấu '=' xảy ra khi \(\begin{cases}x-1=0\\ 2y+1=0\end{cases}\Rightarrow\begin{cases}x=1\\ y=-\frac12\end{cases}\)
Bài 16:
a: \(N=100x^2-20x+1\)
\(=\left(10x\right)^2-2\cdot10x\cdot1+1^2=\left(10x-1\right)^2\)
Khi x=3/10 thì \(N=\left(10\cdot\frac{3}{10}-1\right)^2=\left(3-1\right)^2=2^2=4\)
b: \(P=25x^2-10xy^2+y^4\)
\(=\left(5x\right)^2-2\cdot5x\cdot y^2+\left(y^2\right)^2=\left(5x-y^2\right)^2\)
Khi x=5; y=4 thì \(P=\left(5\cdot5-4^2\right)^2=9^2=81\)
Bài 14:
a: \(81^2=\left(80+1\right)^2=6400+2\cdot80+1=6561\)
b: \(102^2=\left(100+2\right)^2=100^2+2\cdot100\cdot2+2^2=10404\)
c: \(97\cdot103=\left(100-3\right)\left(100+3\right)=100^2-3^2=10000-9=9991\)
