1. х^2+34х-4 = 0
Д (дискриминант) = 34^2-4*(-4) = 1156+16 = 1172
х = -34+корень из 1172 (полность не извлекается, поэтому пусть так остается)/2 = -17+корень из 1172
х = -34-корень из 1172/2 = -17-корень из 1172
2. х^2+24х-6 = 0
Д = 24^2-4*(-6) = 600
х = -24+корень из 600/2 = -12+корень из 600
х = -24-корень из 600/2 = -12-корень из 600
3. х+2 = 16х+2/х
х^2/х+2х/х = 16х^2/х+2/х
х^2+2х = 16х^2+2
16х^2-х^2-2х+2 = 0
15х^2-2х+2 = 0
Д = (-2)^2-4*15*2 = 4-120 = -116
Ответ: действительный корней нет, т.к. дискриминант отрицателен
1)sin20⁰cos10⁰+cos20⁰sin10⁰=
=1/2[sin(20⁰+10⁰)+sin(20⁰-10⁰)]+1/2[sin(10⁰+20⁰)+sin(10⁰-20⁰)]=
=1/2[sin30⁰+sin10⁰]+1/2[sin30⁰+sin(-10⁰)]=sin30⁰+1/2sin10⁰-1/2sin10⁰=
=sin30⁰=1/2;
2)sinπ/5cos4π/5+cosπ/5sin4π/5=
=1/2[sin(π/5+4π/5)+sin(π/5-4π/5)]+1/2[sin(4π/5+π/5)+sin(4π/5-π/5)]=
=1/2[sinπ+sin(-3π/5)]+1/2[sinπ+sin(3π/5]=
=sinπ-1/2sin(3π/5)+1/2sin(3π/5)=
=sinπ=0;
3)cos80⁰cos10⁰+sin80⁰cos10⁰=
=1/2[cos(80⁰-10⁰)+cos(80⁰+10)⁰]+1/2[sin(80⁰+10⁰)+sin(80⁰-10⁰)]=
=1/2[cos70⁰+cos90⁰]+1/2[sin90⁰+sin70⁰]=
=1/2[cos70⁰+0]+1/2[1+sin70⁰]=1/2cos70⁰+1/2sin70⁰+1/2;
4)cos3π/8sinπ/8+cosπ/8sin3π/8=
=1/2[sin(π/8+3π/8)+sin(π/8-3π/8)]+1/2[sin(3π/8+π/8)+sin(3π/8-π/8)]=
=1/2[sin(π/2)+sin(-π/4)]+1/2[sin(π/2)+sin(π/4)]=
=sin(π/2)-1/2sin(π/4)+1/2sin(π/4)=sin(π/2)=1;
<span>sin^2x–5sinx+4=0
D = 25 - 16 = 9
sinx1 = 5 - 3 = 2
sinx2 = 5+3 = 8
наименьший sinx1</span>