1) х^2 - 5х - 24 = ( Х - 8 )( Х + 3 )
D = 25 + 96 = 121 = 11^2
Х1 = ( 5 + 11 ) : 2 = 8
Х2 = ( 5 - 11 ) : 2 = - 3
2) х^2 - 6х - 27 = ( Х - 9 )( x + 3 )
D = 36 + 108 = 144 = 12^2
X1 = ( 6 + 12 ) : 2 = 9
X2 = ( 6 - 12 ) : 2 = - 3
3) ( ( x - 8 )( x + 3 )) / ( ( x - 9 )( x + 3 )) = ( x - 8 ) / ( x - 9 )
По формуле приведения sin (π/2 + 5x) = cos 5x
√2 · cos 2x · cos 5x - cos 2x = 0
cos 2x · (√2 · cos 5x - 1) = 0
cos 2x = 0 или √2 · cos 5x - 1 = 0
2x = π/2 + πn cos 5x = 1/√2
x = π/4 + πn/2 5x = arccos (1/√2) + 2πk или 5x = - arccos (1/√2) + 2πm
5x = π/4 + 2πk 5x = - π/4 + 2πm
x = π/20 + 2πk/5 x = - π/20 + 2πm/5
<span>-9(4+x)=8x-2
-36 -9x -8x = -2
-17x = -2 +36
-17x = 34
x = 34/ -17
x = -2</span>