La suma de los elementos del conjunto solución de
p(x):|9-x|-7x/22-48/11=0
Es:
a)0
b)7
c)7/11
d)48/11
e)7/22
Respuestas
Respuesta:
102/29 + 294/15 = (1530 + 8526) / 435 = (10.056) / 435 = (3.352) / 145 = 23.117
Explicación paso a paso:
DESARROLLO
{|9-x| = 7x/22 + 48/11} ≡
{9-x ≥0 ∧ 9 - x = 7x/22 + 48/11} ∪ {9-x < 0 ∧ -(9-x) = 7x/22 + 48/11}
{9 ≥ x ∧ 9 - 48/11 = 7x/22 + x} ∪ {9 < x ∧ -(9-x) = 7x/22 + 48/11}
{x ≤ 9 ∧ 51/11 = 29x/22} ∪ {x > 9 ∧ -9+x) = 7x/22 + 48/11}
{ x ≤ 9 ∧ 51 = 29x/2} ∪ {x > 9 ∧ -9-48/11 = 7x/22-x}
{x ≤ 9 ∧ 102 = 29x} ∪ {x > 9 ∧ -147/11 = -15x/22}
{x ≤ 9 ∧ 102/29 = x} ∪ {x > 9 ∧ 147 = 15x/2}
{ x ≤ 9∧ x = 102/29} ∪ {x > 9 ∧ 294 = 15x}
{x ≤ 9 ∧ x = 3,5172} ∪ {x > 9 ∧ x = 294/15}
{x ≤ 9 ∧ x=3,5172} ∪ {x > 9 ∧ x = 19.6}
Solución: x_1 = 102/29
Solución: x_2 = 294/15
⟹ x_1 = 102/29 + x_2 = 294/15
102/29 + 294/15 = (1530 + 8526) / 435 = (10.056) / 435 = (3.352) / 145 = 23.117
COMPROBACIÓN DE x_1 = 102/29
|9-x| = 7x/22 + 48/11
|9-102/29| = (7(102/29))/22 + 48/11
|159/29| = (714/29)/22 + 48/11
|159/29| = 714/638 + 48/11
|159/29| = (714*11 + 638*48) / (7.018)
|159/29| = (7.854 + 30.624) / (7.018)
|159/29| = (38.478) / (7.018)
|159/29| = 159/29
159/29 = 159/29
COMPROBACIÓN DE x_2 = 294/15
|9-x| = 7x/22 + 48/11
|9-294/15| = (7(294/15))/22 + 48/11
|(135-294)/15| = ((2.058)/15)/22 + 48/11
|-159/15| = (2.058)/330 + 48/11
159/15 = (2.058*11 + 330*48) / (3.630)
159/15 = (22.638+15.840) / (3.630)
53/5 = (38.478) / (3.630)
53/5 = 53/5
Respuesta:
es 0
Explicación paso a paso: DESTRUIMOS EL VALOR ABSOLUTO
9-X²-7X/22-48/11=0 BUSCAMOS UN MINIMO COMUN EN ESTE CASO 22
22(9)- 22X²-22(7X/22)-22(48/11)= 0
198-22X²-7X-96=0 -198+22X²-7X-96=0
-22X²-7X+102=0 22X²-7X-294=0
X1+X2=-b/a=-7/22 X1+X2=b/a=7/22
-7/22 +7/22=0