1) log (cosπ/4) (x^2-x)≥-2
log(√2/2) (x^2 -x)≥-2 cosπ/4=√2/2; x^2-x>0
log(√2/2) (x^2-x) ≥ log(√2/2) (√2/2)^(-2); √2/2<1<br> {x^2-x≤ 2 (2/√2)^2=4/2=2
{x^2-x>0
x^2-x-2≤0; D=1-4*1*(-2)=9=3^2; x1=(1-3)/2=-1;x2=(1+3)/2=2
+ - +
---------------(-1)-----------------2--------------------->x
/////////////////////////// x⊂[-1;2]
x^2-x>0; x(x-2)>0 + - +
--------0-------------2------------>x
//////////// //////////////// x⊂(0;2)
Общее решение; х⊂(0;2); количество целых-только 1
Ответ 1