Question

Решите уравнение:
$-x^2+2x+2=3+sin^2 pi x$

Answer 1

$begin{cases}-x^2+2x+2=-(x^2-2x+1)+3=-(x-1)^2+3leqslant3\ 3+sin^2pi xgeqslant 3end{cases}Rightarrow\Rightarrowbegin{cases}-(x-1)^2+3=3\ 3+sin^2pi x=3 end{cases}\ boxed{x=1}$