Respuestas
Explicación paso a paso:
c)
(u+2) / (3.u-1) + 1 = (6-u) / (u+1)
(u + 2 + 3.u - 1) / (3.u-1) = (6-u) / (u+1)
(4.u + 1) . ( u+1 ) = (6-u) . (3.u-1)
4.u^2 + 4.u + u + 1 = 18.u - 6 - 3.u^2 + u
7.u^2 - 14.u + 7 = 0
7.u - 7
1.u - 1
(7.u - 7) . ( 1.u- 1) = 0
7.u - 7=0 y 1.u-1 =0
u=1 y u =1
Entonces el valor de u es 1.
e)
x^2 = 5.x - 6
x^2 - 5.x + 6 = 0
x -3
x -2
(x-3) . (x-2) = 0
x-3 = 0 y x-2=0
x =3 y x =2
Entonces los valores de x son 3 y 2
i)
(3) / (x-1) - (5.x) / (x+2) = 1/4
[ 3. (x+2) - 5.x. (x-1) ] / (x-1).(x+2) = 1/4
3. (x+2) - 5.x. (x-1) = (x-1) . (x+2) / 4
3.x + 6 - 5.x^2 + 5.x = (x^2 +2.x - x - 2) / 4
4. (-5.x^2 +8.x +6) = (x^2 + x - 2)
-20.x^2 + 32.x + 24 = x^2 + x - 2
21.x^2 - 31.x - 26 = 0
Aplicamps formula cuadratica:
x1 = [b + (b^2 - 4.a.c)^ (1/2) ] / (2.a)
x1 = [-31 + ((-31)^2 - 4.(21).(-26))^ (1/2) ] / (2.(21))
x1 = [-31 + (961 + 2184)^(1/2) ] / 42
x1 = [-31 + (961 + 2184)^(1/2) ] / 42
x1 = (-31 + 56, 08) / 42
x1 = -0,597
Para x2:
x2 = [b - (b^2 - 4.a.c)^ (1/2) ] / (2.a)
x2 = [-31 - ((-31)^2 - 4.(21).(-26))^ (1/2) ] / (2.(21))
x2 = [-31 - (961 + 2184)^(1/2) ] / 42
x2 = [-31 - (961 + 2184)^(1/2) ] / 42
x2 = (-31 - 56, 08) / 42
x2 = 2,073