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PRELIMINARES

Valor numérico de expresiones compuestas
Ejercicio 13
Para este conjunto de problemas se debe reemplazar cada letra por su respectivo valor numérico y realizar las operaciones correspondientes
Hallar, el valor numérico de las expresiones siguientes para: a=1, b=2, c=3, d=4, m= 1 2 , n= 2 3 ,p= 1 4 , x=0
  1. (a+b ) cd=(1+2 ) 34=3( 3 ) 4=94=5
  2. (a+b ) (ba ) =(1+2 ) (21 ) =3( 1 ) =3
  3. (bm ) (cn ) +4 a 2 = (2 1 2 ) (3 2 3 ) +4(1 ) 2 = ( 41 2 ) ( 92 3 ) +4 = 3 2 ( 7 3 ) +4 = 7 2 +4= 7+8 2 = 15 2 7 1 2
  4. (2m+3n ) (4p+ b 2 ) = ( 2 1 2 + 3 2 3 ) ( 4 1 4 + 2 2 ) = (1+2 ) (1+4 ) = 3( 5 ) = 15
  5. (4m+8p ) ( a 2 + b 2 ) (6nd ) = ( 1 2 + 1 4 ) ( 1 2 + 2 2 ) ( 2 3 4 ) = = 0
  6. (cb ) (dc ) (ba ) (mp ) = (32 ) (43 ) (21 ) ( 1 2 1 4 ) = ( 1 ) ( 1 ) ( 1 ) ( 21 4 ) = 1 4
  7. b 2 (c+d ) a 2 (m+n ) +2x = 2 2 (3+4 ) 1 2 ( 1 2 + 2 3 ) +2( 0 ) = 4( 7 ) ( 3+4 6 ) = 28 7 6 = 1687 6 = 161 6 26 5 6
  8. 2mx+6( b 2 + c 2 ) 4 d 2 = +6( 2 2 + 3 2 ) 4(4 ) 2 = 6( 13 ) 64 = 7864 = 14
  9. ( 8m 9n + 16p b ) a = ( 1 2 2 3 + 1 4 2 ) ( 1 ) = ( + 2 ) = 2 3 +2= 2+6 3 = 8 3 2 2 3
  10. x+m( a b + d c c a ) = 0+ 1 2 ( 1 2 + 4 3 3 1 ) = 1 2 (1+643 ) = 2 = 31
  11. 4(m+p ) a + a 2 + b 2 c 2 = 4( 1 2 + 1 4 ) 1 ÷ 1 2 + 2 2 3 2 = 4 ( 2+1 4 ) ÷ 5 9 = 3 ÷ 5 9 3 5 9 = 27 5 5 2 5
  12. (2m+3n+4p ) (8p+6n4m ) (9n+20p ) = ( 2 1 2 + 3 2 3 + 4 1 4 ) ( 1 4 + 2 3 1 2 ) ( 2 3 + 1 4 ) = (1+2+1 ) ( 2 +4 2 ) (6+5 ) = ( 4 ) ( 4 ) ( 11 ) = 176
  13. c 2 (m+n ) d 2 (m+p ) + b 2 (n+p ) = 3 2 ( 1 2 + 2 3 ) 4 2 ( 1 2 + 1 4 ) + 2 2 ( 2 3 + 1 4 ) = ( 3+4 ) ( 2+1 4 ) + 4 ( 8+3 ) = 3( 7 2 ) 4( 3 ) + 11 3 = 21 2 12+ 11 3 = 6372+22 6 = 13 6 2 1 6
  14. ( c 2 + d 2 a ÷ 2 d ) m = ( c 2 + d 2 a 2 d ) m = ( 3 2 + 4 2 1 2 4 ) 1 2 = ( 25 2 2 ) 1 2 = 5 2 2 1 2
  15. (4p+2b ) (18n24p ) +2(8m+2 ) (40p+a ) = ( 4 1 4 +2( 2 ) ) ( 2 3 1 4 ) +2( 1 2 +2 ) ( 1 4 +1 ) = (1+4 ) (126 ) +2(4+2 ) (10+1 ) = 5( 6 ) +2( 6 ) ( 11 ) = 30+132 = 162
  16. a+ d b db × 5+ 2 m 2 p 2 = 1+ 2 42 × 5+ 2 ( 1 2 ) 2 ( 1 4 ) 2 = 3 2 × 5+ 2 1 4 1 16 = 3 2 × 5+8 1 16 = 3 2 × 13 1 16 = 3 2 × 13( = 312
  17. (a+b ) c 2 +8b m n 2 = (1+2 ) 3 2 +8( 2 ) 1 2 ( 2 3 ) 2 = 3 9+16 1 2 ( 2 3 ) = 3 25 1 3 = 3( 5 ) 1 3 = 15 1 3 = 451 3 = 44 3 14 2 3
  18. ( a+c 2 + 6n b ) ÷ (c+d )p = ( 1+3 2 + 2 3 2 ) ÷ (3+4 ) 1 4 = ( 4 2 + 4 2 ) ÷ 7( 1 2 ) = ( 2 2 + 2 2 ) ÷ 7 2 = 2 7 2 = 4 7
  19. 3(cb ) 32m 2(da ) 16p 2 n = 3(32 ) 1 2 2(41 ) 1 4 2 2 3 = 3( 1 ) ( 4 ) 2( 3 ) ( 2 ) 3 = 12 12 3 = 3
  20. 6abc 2 8b + 3mn 2(ba ) cdnp abc = 6( 1 ) ( 2 ) ( 3 ) 2 8( 2 ) + 3 ( 1 2 ) ( 2 3 ) 2(21 ) 3 (4 ) ( 2 3 ) ( 1 4 ) ( 1 ) (2 ) ( 3 ) = 36 2 16 + 1 2 1 3 = 2 ( 4 ) +( 32 6 ) = 3 4 + 1 6 = 9+2 12 = 11 12
  21. a 2 + b 2 b 2 a 2 +3(a+b ) (2a+3b ) = 1 2 + 2 2 2 2 1 2 +3(1+2 ) (2 × 1+3 × 2 ) = 1+4 41 +3( 3 ) (2+6 ) = 5 3 +72= 5+216 3 = 221 3 73 2 3
  22. b 2 +( 1 a + 1 b ) ( 1 b + 1 c ) + ( 1 n + 1 m ) 2 = 2 2 +( 1 1 + 1 2 ) ( 1 2 + 1 3 ) + ( 1 2 3 + 1 1 2 ) 2 = 4+( 2+1 2 ) ( 3+2 6 ) + ( 3 2 +2 ) 2 = 4+( 3 2 ) ( 5 ) + ( 3+4 2 ) 2 = 4+ 5 4 + ( 7 2 ) 2 = ( 16+5 4 ) + 49 4 = 21 4 + 49 4 = 21+49 4 = 35 2 17 1 2
  23. (2m+3n ) (4p+2c ) 4 m 2 n 2 = ( 2 1 2 + 3 2 3 ) ( 4 1 4 +2 × 3 ) 4 ( 1 2 ) 2 ( 2 3 ) 2 = (1+2 ) (1+6 ) 4 ( 1 4 ) ( 4 9 ) = 3( 7 ) 4 9 = 21 4 9 = 1894 9 = 185 9 20 5 9
  24. b 2 c 3 2abm n bm = 2 2 3 3 2( 1 ) ( 2 ) 1 2 2 3 2 1 2 = 41 4 1 2 2 3 41 2 = 3 81 2 2 3 3 2 = 3 7 2 4 9 = 6 7 4 9 = 5428 63 = 26 63