Ejercicio 81

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CAPITULO VIII

Ecuaciones enteras de primer grado
Ejercicio 81
MISCELANIA
Resolver las siguientes ecuaciones:
  1. 14x(3x2 ) [5x+2(x1 ) ] =0 14x3x+2[5x+2x+1 ] =0 11x+2(4x+3 ) =0 11x+24x3 =0 7x1 =0 7x =1 x = 1 7
  2. (3x7 ) 2 5(2x+1 ) (x2 ) = x 2 [(3x+1 ) ] 9 x 2 42x+495(2 x 2 4x+x2 ) = x 2 +(3x+1 ) 9 x 2 42x+4910 x 2 +15x+10 = x 2 +3x+1 x 2 27x+59 = x 2 +3x+1 27x3x =59+1 30x =58 x = x = 29 15
  3. 6x(2x+1 ) ={5x+[(2x1 ) ] } 6x2x1 ={5x+[2x+1 ] } 4x1 ={5x+2x+1 } 4x1 ={3x+1 } 4x 1 =3x 1 4x3x =0 x =0
  4. 2x+3( x 2 1 ) ={3 x 2 +2(x1 ) 3(x+2 ) } 2x3 x 2 3 ={3 x 2 +2x23x6 } 2x3 x 2 3 ={3 x 2 x8 } 2x 3 x 2 3 = 3 x 2 +x+8 2xx =8+3 x =11
  5. x 2 {3x+[x(x+1 ) +4( x 2 1 ) 4 x 2 ] } =0 x 2 {3x+[ x 2 +x+ 4 x 2 4 4 x 2 ] } =0 x 2 {3x+ x 2 +x4 } =0 x 2 { x 2 +4x4 } =0 x 2 x 2 4x+4 =0 4x =4 x = 4 4 x =1
  6. 3(2x+1 ) (x+3 ) (2x+5 ) 2 =[{3(x+5 ) } +10 x 2 ] 3(2 x 2 +6xx+3 ) (4 x 2 +20x+25 ) =[{3x15 } +10 x 2 ] 6 x 2 +15x+94 x 2 20x25 =[3x+15+10 x 2 ] 10 x 2 5x16 =3x15 10 x 2 5x+3x =1615 2x =1 x = 1 2
  7. (x+1 ) (x+2 ) (x3 ) =(x2 ) (x+1 ) (x+1 ) ( x 2 +3x+2 ) (x3 ) =( x 2 x2 ) (x+1 ) x 3 + 3 x 2 +2x 3 x 2 9x6 = x 3 x 2 2x+ x 2 x2 7x6 =3x2 7x+3x =62 4x =4 x = 4 4 x =1
  8. (x+2 ) (x+3 ) (x1 ) =(x+4 ) (x+4 ) (x4 ) +7 ( x 2 +5x+6 ) (x1 ) =(x+4 ) ( x 2 16 ) +7 x 3 +5 x 2 +6x x 2 5x6 = x 3 16x+4 x 2 64+7 4 x 2 +x6 = 4 x 2 16x+ 4 x 2 57 x+16x =657 17x =51 x = 17 x =3
  9. (x+1 ) 3 (x1 ) 3 =6x(x3 ) [(x+1 ) (x1 ) ] [ (x+1 ) 2 +(x+1 ) (x1 ) + (x1 ) 2 ] =6 x 2 18x [ x +1 x +1 ] [ x 2 + 2x + 1 + x 2 1 + x 2 2x +1 ] =6 x 2 18x 2(3 x 2 +1 ) =6 x 2 18x 6 x 2 +2 = 6 x 2 18x 2 =x x = 1 9
  10. 3 (x2 ) 2 (x+5 ) =3 (x+1 ) 2 (x1 ) +3 Dividiendo la ecuación para 3 (x2 ) 2 (x+5 ) = (x+1 ) 2 (x1 ) +1 ( x 2 4x+4 ) (x+5 ) =( x 2 +2x+1 ) (x1 ) +1 x 3 4 x 2 +4x+5 x 2 20x+20 = x 3 +2 x 2 +x x 2 2x 1 + 1 x 2 16x+20 = x 2 x 16x+x =20 15x =20 x = x = 4 3