Question

ayuda........

1) x^2-6x+1=0

2) 3x^2+10x-25=0

3) x^2+25x=0

4) 2x^2-2x-4=20

5) 5x^2-3x=2

6) x^2-8x+5=5

7) 4x^2+3x-1=0

8) x^2+3x-1=0

Answer 1

Son Ecuaciones Cuadráticas que se solucionan por la Resolvente.

X1,2 = – B ± √(B² – 4AC) ÷ 2A

Donde:

A: coeficiente que acompaña al termino cuadrático.

B: coeficiente que acompaña al termino elevado a la unidad.

C: Coeficiente del término independiente o constante.

1) x² – 6x + 1 = 0  

A = 1; B = – 6; C = 1  

X1,2 = – (– 6) ± √(– 6)² – 4(1)(1) ÷ 2(1)

X1,2 = 6 ± √(36 – 4) ÷ 2

X1,2 = 6 ± √32 ÷ 2

X1,2 = 6 ± 5,66 ÷ 2

X1 = 6 + 5,66 ÷ 2

X1 = 11,66 ÷ 2

X1 = 5,83

X2 = 6 – 5,66 ÷ 2

X2 = 0,34÷ 2

X2 = 0,17

2) 3x² + 10x – 25 = 0  

A = ;3 B = 10; C = – 25

X1,2 = – (10) ± √(10)² – 4(3)( – 25) ÷ 2(3)

X1,2 = – 10 ± √(100 + 300) ÷ 6

X1,2 = – 10 ± √400 ÷ 6

X1,2 = – 10 ± 20 ÷ 6

X1 = – 10 + 20 ÷ 6

X1 = 10 ÷ 6

X1 = 5/3 = 1.66…..

X2 = – 10 – 20 ÷ 6

X2 = – 30 ÷ 6

X2 = – 5

3) x² + 25x = 0  

A = 1; B = 25; C = 0

X1,2 = – (25) ± √(25)² – 4(1)(0) ÷ 2(1)

X1,2 = – 25 ± 25 ÷ 2

X1 = – 25 + 25 ÷ 2

X1 = 0

X2 = – 25 – 25 ÷ 2

X2 = – 50 ÷ 2

X2 = – 25

4) 2x² – 2x – 4 = 20  

Ordenando la ecuación queda:

2x² – 2x – 24 = 0

A = 2; B = – 2; C = – 24

X1,2 = – (– 2) ± √(– 2)² – 4(2)(– 24) ÷ 2(2)

X1,2 = 2 ± √(4 + 192) ÷ 4

X1,2 = 2 ± √196 ÷ 4

X1,2 = 2 ± 14 ÷ 4

X1 = 2 + 14 ÷ 4

X1 = 16 ÷ 4

X1 = 4

X2 = 2 – 14 ÷ 4

X2 = – 12 ÷ 4

X2 = – 3

5) 5x² – 3x = 2

Ordenando la ecuación queda:

5x² – 3x – 2 = 0

A = 5; B = – 3; C = – 2

X1,2 = – (– 3) ± √(– 3)² – 4(5)(– 2) ÷ 2(5)

X1,2 = 3 ± √(9 + 40) ÷ 10

X1,2 = 3 ± √49 ÷ 10

X1,2 = 3 ± 7 ÷ 10

X1 = 3 + 7 ÷ 10

X1 = 10 ÷ 10

X1 = 1

X2 = 3 – 7 ÷ 10

X2 = – 4 ÷ 10

X2 = – 2/5 = – 0,4

6) x² – 8x + 5 = 5  

Ordenando la ecuación queda:

x² – 8x + 5 – 5 = 0

x² – 8x = 0

A = 1; B = – 8; C = 0

X1,2 = – (– 8) ± √(– 8)² – 4(1)(0) ÷ 2(1)

X1,2 = 8 ± √(64) ÷ 2

X1,2 = 8 ± 8 ÷ 2

X1 = 16 ÷ 2

X1 = 8

X2 = 8 – 8 ÷ 2

X2 = 0

7) 4x² + 3x – 1 = 0  

A = 4; B = 3; C = – 1

X1,2 = – (3) ± √(3)² – 4(4)( – 1) ÷ 2(4)

X1,2 = – 3 ± √(9 + 16) ÷ 8

X1,2 = – 3 ± √25 ÷ 8

X1,2 = – 3 ± 5 ÷ 8

X1 = – 3 + 5 ÷ 8

X1 = 2 ÷ 8

X1 = 1/4 = 0,25

X2 = – 3 – 5 ÷ 8

X2 = – 8 ÷ 8

X2 = – 1

8) x² + 3x – 1 = 0

A = 1; B 3= ; C = – 1

X1,2 = – (3) ± √(3)² – 4(1)(– 1) ÷ 2(1)

X1,2 = – 3 ± √(9 + 4) ÷ 2

X1,2 = – 3 ± √13 ÷ 2

X1,2 = – 3 ± 3,6 ÷ 2

X1 = – 3 + 3,6 ÷ 2

X1 = 0,6 ÷ 2

X1 = 0,3

X2 = – 6,6 ÷ 2

X2 = – 3,3