Question

Решите пожалуйста
5x²-3x-2=0
2x²-5x+3=0
x²+3x+1=0
2x²-9x+4=0
3x+8x-3=0
2x-7x+3=0

Answer 1

1) 5x² - 3x-2= 0
D= b²- 4ac
D= 9+ 40= 49
√D= 7
x₁= $frac{-b+ sqrt{D} }{2a} = frac{3+7}{10}= 1$
x₂= $frac{-b- sqrt{D} }{2a} = frac{3-7}{10} = -frac{4}{10}= - frac{2}{5}$
Ответ: x₁= 1; x₂= $frac{2}{5}$
2) 2x²- 5x+ 3= 0
D= b² -4ac
D= 25- 24 = 1
√D= 1
x₁= $frac{-b+ sqrt{D} }{2a} = frac{5+1}{4} = 1,5$
x₂= $frac{-b- sqrt{D} }{2a}= frac{5-1}{4} = 1$
Ответ: x₁= 1,5 ; x₂= 1
3) x²+ 3x+ 1= 0
D= b² -4ac
D= 9- 4= 5
√D= √5
x₁= $frac{-b+ sqrt{D} }{2a} = frac{-3+ sqrt{5} }{2}$
x₂= $frac{-b- sqrt{D} }{2a} = frac{3- sqrt{5} }{2}$
4) 2x² -9x+ 4 = 0
D= b²  -4ac
D= 81 - 32= 49
√D= 7
x₁= $frac{-b+ sqrt{D} }{2a} = frac{9+ 7}{4} = 4$
x₂=$frac{-b- sqrt{D} }{2a} = frac{9-7}{4} = frac{1}{2}$
5) 3x² + 8x- 3=0
D= b² -4ac
D= 64+ 36= 100
√D= 10
x₁= $frac{-b+ sqrt{D} }{2a} = frac{-8+10}{6} = frac{2}{6} = frac{1}{3}$
x₂= $frac{-b- sqrt{D} }{2a} = frac{-8-10}{6} = -3$
6) 2x² -7x+ 3= 0
D= b² -4ac
D= 49- 24 = 25
√D= 5
x₁= $frac{-b+ sqrt{D} }{2a} = frac{7+5}{4} = 3$
x₂= $frac{-b- sqrt{D} }{2a} = frac{7-5}{4} = frac{1}{2}$