a: \(x+y=4\)
=>\(\left(x+y\right)^2=4^2=16\)
=>\(x^2+y^2+2xy=16\)
=>\(2xy=16-10=6\)
=>xy=3
\(x^3+y^3=\left(x+y\right)\left(x^2+y^2-xy\right)\)
\(=4\left(10-3\right)=4\cdot7=28\)
b:
\(A=3x-x^2-3\)
\(=-\left(x^2-3x+3\right)\)
\(=-\left(x^2-3x+\dfrac{9}{4}+\dfrac{3}{4}\right)\)
\(=-\left(x-\dfrac{3}{2}\right)^2-\dfrac{3}{4}< =-\dfrac{3}{4}< 0\forall x\)