CAPITULO V
División
Hallar el valor numérico
- Ejercicio 60
Hallar el volor numérico de las expresiones siguientes para
a=–1,b=2,c=–
1
2
- a 2 –2ab+ b 2 = ( –1 ) 2 –2( –1 ) ( 2 ) + ( 2 ) 2 =1+4+4 =9
- 3 a 3 –4 a 2 b+3a b 2 – b 3 =3 ( –1 ) 3 –4 ( 1 ) 2 ( 2 ) +3( –1 ) ( 2 ) 2 – ( 2 ) 3 =3( –1 ) –8–12–8 =–3–28 =–31
- a 4 –3 a 3 +2ac–3bc = ( –1 ) 4 –3 ( –1 ) 3 + 2 ( –1 ) ( – 1 2 ) –3( 2 ) ( – 1 2 ) =1+3+1+3 =8
- a 5 –8 a 4 c+16 a 3 c 2 –20 a 2 c 3 +40a c 4 – c 5 = ( –1 ) 5 – ( –1 ) 4 ( – 1 2 ) +16 ( –1 ) 3 ( – 1 2 ) 2 –20 ( –1 ) 2 ( – 1 2 ) 3 +40( –1 ) ( – 1 2 ) 4 – ( – 1 2 ) 5 =–1+4–( 1 4 ) –( – 1 ) –( 1 ) + 1 32 =–1+ 4 – 4 + 5 2 – 5 2 + 1 32 = –32+1 32 =– 31 32
- ( a–b ) 2 + ( b–c ) 2 – ( a–c ) 2 = ( –1–2 ) 2 + ( 2–[ – 1 2 ] ) 2 – ( –1–[ – 1 2 ] ) 2 = ( –3 ) 2 + ( 2+ 1 2 ) 2 – ( –1+ 1 2 ) 2 =9+ ( 4+1 2 ) 2 – ( –2+1 2 ) 2 =9+ ( 5 2 ) 2 – ( – 1 2 ) 2 =9+ 25 4 – 1 4 = 36+25–1 4 = 4 =15
- ( b+a ) 3 – ( b–c ) 3 – ( a–c ) 3 = ( 2+[ –1 ] ) 3 – ( 2–[ – 1 2 ] ) 3 – ( –1–[ – 1 2 ] ) 3 = ( 2–1 ) 3 – ( 2+ 1 2 ) 3 – ( –1+ 1 2 ) 3 = ( 1 ) 3 – ( 4+1 2 ) 3 – ( –2+1 2 ) 3 =1– ( 5 2 ) 3 – ( – 1 2 ) 3 =1– 125 8 + 1 8 = 8–125+1 8 =– =– 29 2 =–14 1 2
- ab c + ac b – bc a = ( –1 ) ( 2 ) – 1 2 + ( –1 ) ( – 1 2 ) 2 – ( 2 ) ( – 1 2 ) ( –1 ) =4+ 1 4 –1 = 16+1–4 4 = 13 3 =3 1 4
- ( a+b+c ) 2 – ( a–b–c ) 2 +c = ( [ –1 ] +2+[ – 1 2 ] ) 2 – ( [ –1 ] –2–[ – 1 2 ] ) 2 +( – 1 2 ) = ( 1– 1 2 ) 2 – ( –3+ 1 2 ) 2 – 1 2 = ( 2–1 2 ) 2 – ( –6+1 2 ) 2 – 1 2 = ( 1 2 ) 2 – ( – 5 2 ) 2 – 1 2 = 1 4 – 25 4 – 1 2 = 1–25–2 4 =– =– 13 2 =–6 1 2
- 3( 2a+b ) –4a( b+c ) –2c( a–b ) =3[ 2( –1 ) +2 ] –4( –1 ) [ 2+( – 1 2 ) ] – 2 ( – 1 2 ) [ ( –1 ) –2 ] =+4( 4–1 2 ) +( –3 ) =( 3 2 ) –3 =6–3 =3
Hallar el valor numérico de las expresiones siguientes para
a=2,b=
1
3
,x=–2,y=–1,m=3,n=
1
2
- x 4 8 – x 2 y 2 + 3x y 2 2 – y 3 = ( –2 ) 4 8 – ( –2 ) 2 ( –1 ) 2 + 3( – 2 ) ( –1 ) 2 2 – ( –1 ) 3 =2+2–3+1 =2
- ( a–x ) 2 + ( x–y ) 2 +( x 2 – y 2 ) ( m+x–n ) = ( 2–[ –2 ] ) 2 + ( –2–[ –1 ] ) 2 +( [ –2 ] 2 – [ –1 ] 2 ) ( 3+[ –2 ] – 1 2 ) = ( 4 ) 2 + ( –1 ) 2 +( 4–1 ) ( 6–4–1 2 ) =16+1+3( 1 2 ) =17+ 3 2 = 34+3 2 = 37 2 =18 1 2
- –( x–y ) +( x 2 + y 2 ) ( x–y–m ) +3b( x+y+n ) =–[ –2–( –1 ) ] +[ ( –2 ) 2 + ( –1 ) 2 ] [ –2–( –1 ) –3 ] + 3 ( 1 3 ) ( –2–1+ 1 2 ) =–[ –2+1 ] +[ 4+1 ] [ –5+1 ] +( –4–2+1 2 ) =1+5( –4 ) +( – 5 2 ) =1–20– 5 2 = 2–40–5 2 =– 43 2 =–21 1 2
- ( 3x–2y ) ( 2n–4m ) +4 x 2 y 2 – x–y 2 =( 3( –2 ) –2( –1 ) ) ( 2 ( 1 2 ) –4( 3 ) ) +4 ( –2 ) 2 ( –1 ) 2 – –2–( –1 ) 2 =( –6+2 ) ( 1–12 ) +4( 4 ) ( 1 ) – –2+1 2 =–4( –11 ) +16+ 1 2 =44+16+ 1 2 = 88+32+1 2 = 121 2 =60 1 2
- 4x 3y – x 2 2+ y 3 +( 1 n – 1 b ) x+ x 4 –m = 4( –2 ) 3( –1 ) – ( –2 ) 3 2+ ( –1 ) 3 +( 1 1 2 – 1 1 3 ) ( –2 ) + ( –2 ) 4 –3 = 8 3 + 8 2–1 +( 2–3 ) ( –2 ) +16–3 = 8 3 +8+( –1 ) ( –2 ) +13 = 8 3 +21+2 = 8+63+6 3 = 77 3 =25 2 3
- x 2 ( x–y+m ) –( x–y ) ( x 2 + y 2 –n ) + ( x+y ) 2 ( m 2 –2n ) = ( –2 ) 2 [ –2–( –1 ) +3 ] –[ –2–( –1 ) ] [ ( –2 ) 2 + ( –1 ) 2 – 1 2 ] + [ –2+( –1 ) ] 2 [ 3 2 – 2 ( 1 2 ) ] =4( –2+1+3 ) –( –2+1 ) ( 4+1– 1 2 ) + ( –2–1 ) 2 ( 9–1 ) =4( 2 ) –( –1 ) ( 8+2–1 2 ) + ( –3 ) 2 ( 8 ) =8+ 9 2 +72 = 16+9+144 2 = 169 2 =84 1 2
- 3a x + 2y m + 3n y – m n +2( x 3 – y 2 +4 ) = 3( 2 ) – 2 + 2( –1 ) 3 + 3( 1 2 ) –1 – 3 1 2 +2[ ( –2 ) 3 – ( –1 ) 2 +4 ] =–3– 2 3 – 3 2 –6+2( –8–1+4 ) =–9– 2 3 – 3 2 +2( –5 ) = –54–4–9–60 6 =– 127 6 =–21 1 6