a)
[tex]\it |a-2|+|7-b| \leq0\ \ \ \ (1)\\ \\ |a-2|\geq0,\ |7-b|\geq0 \Rightarrow |a-2|+|7-b| \geq0\ \ \ \ (2)\\ \\ (1),(2)\Rightarrow|a-2|+|7-b|=0 \Rightarrow \begin{cases}\it a-2=0\Rightarrow a=2\\ \\ \it 7-b=0\Rightarrow b=7\end{cases}[/tex]
b)
[tex]\it m_a=\dfrac{a+b}{2} =\dfrac{2+7}{2}=\dfrac{9}{2}=4,5[/tex]
c)
[tex]\it m_p=\dfrac{4\cdot a+1\cdot b}{4+1} =\dfrac{4\cdot2+1\cdot7}{5}=\dfrac{15}{5}=3[/tex]
d)
[tex]\it a^3-b=2^3-7=8-7=1\\ \\ (a^3-b)^{2019} =1^{2019} =1[/tex]
