1-2sin²√x+√5-2sin√x+√2sin√x-1≤0
2sin²√x+(2-√2)*sinx-√2≥0
sin√x=a
2a²+(2-√2)a-√2≥0
D=(2-√2)²+8√2=2-4√2+2+8√2=(2+√2)²
a1=(-2+√2-2-√2)/4=-1 U a2=(-2+√2+2+√2)/4=√2/2
a≤-1 ⇒sin√x≤-1⇒sin√x=-1⇒√x=-π/2+2πk нет решения
a≥√2/2⇒sin√x≥√2/2⇒π/4+2πk≤√x≤3π/4+2πk⇒
π²/16+π²k+4π²π²≤x≤9π²/16+3π²k+4π²k²,k∈z