Решите квадрат уравнение (20-22): 5.20. a) x2-x- 90 = 0; B) 4x² - x - 3 = 0​​

Ответ:

a) x=-9,\ x=10

б) x=- \frac{ 3 }{ 4 },\ x=1

Объяснение:

a)

x^{2} - x - 90 =0\\\\ a=1 ,\ \ b=-1 ,\ \ c=-90\\\\D = b^2 - 4ac = ( - 1)^2 - 4\cdot1\cdot( - 90) = 1 + 360 = 361\\\\\\\sqrt{D} =\sqrt{361} = 19\\\\x_1=\frac{-b-\sqrt{D}}{2a}=\frac{1-19}{2\cdot1}=\frac{-18 }{2 }=-9\\\\\\ x_2=\frac{-b+\sqrt{D}}{2a}=\frac{1+19}{2\cdot1}=\frac{20}{2}=10

б)

4x^{2} - x - 3 =0\\\\ a=4 ,\ \ b=-1 ,\ \ c=-3\\\\D = b^2 - 4ac = ( - 1)^2 - 4\cdot4\cdot( - 3) = 1 + 48 = 49\\\\\\\sqrt{D} =\sqrt{49} = 7\\\\x_1=\frac{-b-\sqrt{D}}{2a}=\frac{1-7}{2\cdot4}=\frac{-6 }{8 }=- \frac{ 3 }{ 4 } \\\\\\ x_2=\frac{-b+\sqrt{D}}{2a}=\frac{1+7}{2\cdot4}=\frac{8}{8}=1