Question

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1) 3x²- х = 24

2)4x²=-4-1

3)-25=10х+ x²

Answer 1

1) 3х^2-х=24
3х^2-х-24=0
D=(-1) ^2-4×3×(-24) =1+288=289
x=1+-17 /6
х1=3, х2= -2 2/3

3) -25=10+х^2
-х^2-10х-25=0
D=(-10) ^2-4×(-1) ×(-25) =100-100=0
x= -10/2=-5

Answer 2

$3 {x}^{2} - x = 24 \\ 3 {x}^{2} - x - 24 = 0 \\ a = 3 \: \: \: b = - 1 \: \: \: c = - 24 \\ d = {b}^{2} - 4ac = {( - 1)}^{2} - 4 \times 3 \times ( - 24) = 1 + 240 + 48 = 289 = {17}^{2} \\ x1 = \frac{1 + 17}{2 \times 3} = \frac{18}{6} = 3 \\ x2 = \frac{1 - 17}{6} = \frac{ - 16}{6} = - \frac{8}{3}$



$- 4 {x}^{2} = - 4 - 1 \\ - 4 {x}^{2} + 4 + 1 = 0 \\ - 4 {x}^{2} + 5 = 0 \\ a = - 4 \: \: \: \: b = 0 \: \: \: \: c = 5 \\ d = {0}^{2} - 4 \times ( - 4) \times 5 = 80 ={( 4 \sqrt{5} )}^{2} \\ x1 = \frac{0 + 4 \sqrt{5} }{ - 8} = - \frac{ \sqrt{5} }{2} \\ x2 = \frac{ \sqrt{5} }{2}$

$- 25 = 10x + {x}^{2} \\ {x}^{2} + 10x + 25 = 0 \\ d = 100 - 4 \times 1 \times 25 = 0 \\ x1 = x2 = \frac{ - 10 + 0}{2} = - 5$