1)
12у² + 16у - 3 = 0,
Д = 16² - 4*12*(-3) = 256 + 144 = 400,
у1 = (-16+20) / 2*12 = 4/24 = 1/6,
у2 = (-16-20) / 2*12 = -36/24 = -1,5,
2)
2у² - 5у - 3 = 0,
Д = (-5)² - 4*2*(-3) = 25 + 24 = 49,
у1 = (5+7) / 2*2 = 12/4 = 3,
у2 = (5-7) / 2*2 = -2/4 = -0,5,
3)
5а² + 9а + 4 = 0,
Д = 9² - 4*5*4 = 81 - 80 = 1,
а1 = (-9+1) / 2*5 = -8/10 = -0,8,
а2 = (-9-1) / 2*5 = -10/10 = -1,
4)
а² + 9а + 4 = 0,
Д = 9² - 4*1*4 = 81 - 16 = 65,
а1 = (-9 + √65)/2,
а2 = (-9 - √65)/2 или -(9 + √65)/2
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Answers & Comments
1)
12у² + 16у - 3 = 0,
Д = 16² - 4*12*(-3) = 256 + 144 = 400,
у1 = (-16+20) / 2*12 = 4/24 = 1/6,
у2 = (-16-20) / 2*12 = -36/24 = -1,5,
2)
2у² - 5у - 3 = 0,
Д = (-5)² - 4*2*(-3) = 25 + 24 = 49,
у1 = (5+7) / 2*2 = 12/4 = 3,
у2 = (5-7) / 2*2 = -2/4 = -0,5,
3)
5а² + 9а + 4 = 0,
Д = 9² - 4*5*4 = 81 - 80 = 1,
а1 = (-9+1) / 2*5 = -8/10 = -0,8,
а2 = (-9-1) / 2*5 = -10/10 = -1,
4)
а² + 9а + 4 = 0,
Д = 9² - 4*1*4 = 81 - 16 = 65,
а1 = (-9 + √65)/2,
а2 = (-9 - √65)/2 или -(9 + √65)/2