Ответы на вопрос:
2sin²2x - 5cos2x = cos²2x 2(1 - cos²2x) - 5cos2x - cos²2x = 0 2 - 2cos²2x - 5cos2x - cos²2x = 0 - 3cos²2x - 5cos2x + 2 = 0 3cos²2x + 5cos2x - 2 = 0 сделаем замену cos2x = m , - 1 ≤ m ≤ 1 3m² + 5m - 2 = 0 d = 5² - 4 * 3 * (- 2) = 25 + 24 = 49 -посторонний корень cos2x = 2x = + - arccos +2πn , n ∈ z x = + - n ∈ z
9x² + 19x - 24 = 9( x - 8/9 )( x + 3 ) d = 361 + 864 = 1225 = 35² x1 = ( - 19 + 35 ) : 18 = 16/18 = 8/9 x2 = ( - 19 - 35 ) : 18 = - 54 : 18 = - 3 36x² - 59x + 24 = 36(x - 8/9 )( x - 6/8 ) d = 3481 - 3456 = 25 = 5² x1 = ( 59 + 5 ) : 72 = 64/72 = 8/9 x2 = ( 59 - 5 ) : 72 = 54/72 = 6/8 ( ( 9( x - 8/9 )( x + 3 )) / ( 36( x - 8/9 )( x - 6/8 )) = ( x + 3 )/( 4( x - 6/8 )) = = ( x + 3 ) / ( 4x - 3 ) ответ ( x + 3 ) / ( 4x - 3 )
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