Đáp án:
$\\$
`a,`
$\bullet$ `P (x) = 5x^3 - 3x + 7 -x`
`-> P(x) = 5x^3 + (-3x-x) + 7`
`-> P (x)=5x^3 - 4x + 7`
$\bullet$ `Q(x) = -5x^3 + 2x - 3 + 2x -x^2-2`
`-> Q (x) = -5x^3 + (2x+2x) -x^2 + (-3-2)`
`-> Q (x) = -5x^3 + 4x - x^2 - 5`
`-> Q (x) = -5x^3 - x^2 + 4x-5`
$\bullet$ `M (x)=P(x) + Q (x)`
`-> M (x) = (5x^3 - 4x + 7) + (-5x^3 - x^2 + 4x-5)`
`-> M (x) = 5x^3 - 4x + 7 -5x^3 - x^2 + 4x-5`
`-> M (x) = (5x^3 -5x^3) + (-4x+4x) - x^2 + (7-5)`
`->M (x) = -x^2 + 2`
$\bullet$ `N (x) = P (x)-Q (x)`
`-> N (x) = (5x^3 - 4x + 7) - (-5x^3 - x^2 + 4x-5)`
`-> N (x) = 5x^3 - 4x + 7 + 5x^3 + x^2 - 4x +5`
`-> N (x) = (5x^3 + 5x^3) + (-4x-4x) + (7+5) + x^2`
`-> N (x) = 10x^3 - 8x + 12 + x^2`
$\\$
`b,`
$\bullet$ `M (x) = -x^2+2`
Cho `M(x)=0`
`-> -x^2+2=0`
`-> -x^2=0-2`
`->-x^2=-2`
`->x^2=2`
`->` \(\left[ \begin{array}{l}x^2=(\sqrt{2})^2\\x^2=(-\sqrt{2})^2\end{array} \right.\)
`->` \(\left[ \begin{array}{l}x=\sqrt{2}\\x=-\sqrt{2}\end{array} \right.\)
Vậy `x=\sqrt{2},x=-\sqrt{2}` là 2 nghiệm của `M (x)`
