1/
a,\(A=x-x^2=-x^2+x=-\left(x^2-x+\frac{1}{4}\right)+\frac{1}{4}=-\left(x-\frac{1}{2}\right)^2+\frac{1}{4}\)
Vì \(-\left(x-\frac{1}{2}\right)^2\le0\Rightarrow A=-\left(x-\frac{1}{2}\right)^2+\frac{1}{4}\le\frac{1}{4}\)
Dấu "=" xảy ra <=>x=1/2
Vậy Amax=1/4 khi x=1/2
b, \(B=2x-2x^2-5=-2x^2+2x-5\)
\(\Rightarrow2B=-4x^2+4x-10=-\left(4x^2-4x+1\right)-9=-\left(2x-1\right)^2-9\)
Vì \(-\left(2x-1\right)^2\le0\Rightarrow2B=-\left(2x-1\right)^2-9\le-9\Rightarrow B\le\frac{-9}{2}\)
Dấu "=" xảy ra <=>x=1/2
Vậy Bmax=-9/2 khi x=1/2
2/
\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)=2^{32}-1\)
