Косинус двойного угла <u><em> cos2α=cos²α-sin²α
sin</em></u>²<u><em>x+cos²x=1</em></u><u><em /></u><em /> (основное тригонометрическое тождество), <u><em>
</em></u><u><em>cos²x=1-sin²x
</em></u><em>
cos</em>²x-sin²x-sin²x=0.25
1-sin²x-2sin²x=0.25
-3sin²x=-0.75
sin²x=0,25
sinx=0.5 sinx=-0.5
sinx=1/2 sinx=-1/2
x=π/6 x=-π/6
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1.5x -36 -5x -120 =23
-3.5x -156 =23
-3.5x =23+156
-3.5x =179
-x =179 : 35/10
x =( -179*10)/35
х =(-179*2)/7
x =(-51 целая 1/7)
5x² + 3x - 8 = 0
D = b² - 4ac = 9 - 4 × 5 × (-8) = 9 + 160 = 169 = 13²
x1 = ( - 3 + 13) / 10 = 1
x2 = ( - 3 - 13) / 10 = - 1,6
Ответ: x1 = 1, x2 = - 1,6.
(2x + 3)( 3x + 1) = 11x + 30
6x² + 11x + 3 = 11x + 30
6x² + 11x - 11x = 30 - 3
6x² = 27
6x² - 27 = 0
2x² - 9 = 0
2x² = 9
x² = 4,5
x1,2 = +/-√4,5
Ответ: x1,2 = +/-√4,5
x² + 4x - 2 = 0
D = b² - 4ac = 16 - 4 × (-2) = 16 + 8 = 24
x1 = ( - 4 + 2√6) / 2 =-2(2-√6)/2 = - (2 - √6) = - 2 + √6
x2 = ( - 4 - 2√6) / 2 =-2(2 + √6)/2 = -(2 + √6) = - 2 - √6
Ответ: x1 = - 2 + √6, x2 = - 2 - √6.
<span>2d-4y</span> - <span>7d+3y </span> = <span>(2d-4y)*( 2d-3y)</span><span>-( 7d+3y )*( 2d-3y )</span> =