Question

Hallar el valor de x de las ecuaciones cuadráticas por factorización o completando cuadrados según sea necesario.
1. x2 + 6x + 9 = 0
2. 1/2x2 - 10x = 0
3. x2 - 7x + 2 = 0
4. 3/ x - 4 + x - 3/ x = 2

Answer 1

Respuesta:

1) S={-3}

1) S={-3}2) S={20}

1) S={-3}2) S={20}3) S= {7/2 - √41/2; 7/2 + √41/2}

1) S={-3}2) S={20}3) S= {7/2 - √41/2; 7/2 + √41/2}4) S = {-2;6}

Explicación paso a paso:

1) x2 + 6x + 9 = 0

(x+3)^2 = 0

x+3 = 0

x = -3

2) 1/2x2 - 10x = 0

x.(1/2 x - 10) = 0

x = 0

1/2 x - 10 = 0

1/2 x = 10

x = 10 . 2

x = 20

3) x2 - 7x + 2 = 0

(x2 - 7x + 49/4) - 49/4 + 2 = 0

[(x - 7/2)^2] -41/4 = 0

(x- 7/2)^2 = 41/4

|x - 7/2| = √(41/4)

x - 7/2 = √41/2

x = 7/2 + √41/2

x - 7/2 = - √41/2

x = 7/2 - √41/2

4) 3/ x - 4 + x - 3/ x = 2

(x-3)/x = 2 - 3/(x-4)

x-3 = [2 - 3/(x-4)] . x

x-3 = 2x - 3x/(x-4)

x-3 = [2x(x-4)-3x]/(x-4)

x-3 = (2x^2-8x-3x)/(x-4)

(x-3).(x-4) = 2x^2 - 11x

x^2-7x+12 - 2x^2 + 11x = 0

-x^2+4x+12= 0

x^2 - 4x - 12 = 0

(x^2-4x+4)-4-12= 0

(x-2)^2 - 16 = 0

(x-2)^2 = 16

|x-2|=√16

|x-2|=4

x-2=4

x= 6

x-2=-4

x=-2