CAPITULO VIII
Ecuaciones enteras de primer grado
Ecuaciones enteras de primer grado
- Ejercicio 81
- MISCELANIA
Resolver las siguientes ecuaciones:
- 14x–( 3x–2 ) –[ 5x+2–( x–1 ) ] =0 14x–3x+2–[ 5x+2–x+1 ] =0 11x+2–( 4x+3 ) =0 11x+2–4x–3 =0 7x–1 =0 7x =1 x = 1 7
- ( 3x–7 ) 2 –5( 2x+1 ) ( x–2 ) =– x 2 –[ –( 3x+1 ) ] 9 x 2 –42x+49–5( 2 x 2 –4x+x–2 ) =– x 2 +( 3x+1 ) 9 x 2 –42x+49–10 x 2 +15x+10 =– x 2 +3x+1 – x 2 –27x+59 =– x 2 +3x+1 –27x–3x =–59+1 –30x =–58 x = – – x = 29 15
- 6x–( 2x+1 ) =–{ –5x+[ –( –2x–1 ) ] } 6x–2x–1 =–{ –5x+[ 2x+1 ] } 4x–1 =–{ –5x+2x+1 } 4x–1 =–{ –3x+1 } 4x– 1 =3x– 1 4x–3x =0 x =0
- 2x+3( – x 2 –1 ) =–{ 3 x 2 +2( x–1 ) –3( x+2 ) } 2x–3 x 2 –3 =–{ 3 x 2 +2x–2–3x–6 } 2x–3 x 2 –3 =–{ 3 x 2 –x–8 } 2x– 3 x 2 –3 =– 3 x 2 +x+8 2x–x =8+3 x =11
- 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 +x–4 } =0 x 2 –{ x 2 +4x–4 } =0 x 2 – x 2 –4x+4 =0 –4x =–4 x = – 4 – 4 x =1
- 3( 2x+1 ) ( –x+3 ) – ( 2x+5 ) 2 =–[ –{ –3( x+5 ) } +10 x 2 ] 3( –2 x 2 +6x–x+3 ) –( 4 x 2 +20x+25 ) =–[ –{ –3x–15 } +10 x 2 ] –6 x 2 +15x+9–4 x 2 –20x–25 =–[ 3x+15+10 x 2 ] – 10 x 2 –5x–16 =–3x–15– 10 x 2 –5x+3x =16–15 –2x =1 x =– 1 2
- ( x+1 ) ( x+2 ) ( x–3 ) =( x–2 ) ( x+1 ) ( x+1 ) ( x 2 +3x+2 ) ( x–3 ) =( x 2 –x–2 ) ( x+1 ) x 3 + 3 x 2 +2x– 3 x 2 –9x–6 = x 3 – x 2 –2x+ x 2 –x–2 –7x–6 =–3x–2 –7x+3x =6–2 –4x =4 x =– 4 4 x =–1
- ( x+2 ) ( x+3 ) ( x–1 ) =( x+4 ) ( x+4 ) ( x–4 ) +7 ( x 2 +5x+6 ) ( x–1 ) =( x+4 ) ( x 2 –16 ) +7 x 3 +5 x 2 +6x– x 2 –5x–6 = x 3 –16x+4 x 2 –64+7 4 x 2 +x–6 = 4 x 2 –16x+ 4 x 2 –57 x+16x =6–57 17x =–51 x =– 17 x =–3
- ( x+1 ) 3 – ( x–1 ) 3 =6x( x–3 ) [ ( x+1 ) –( x–1 ) ] [ ( x+1 ) 2 +( x+1 ) ( x–1 ) + ( x–1 ) 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
- 3 ( x–2 ) 2 ( x+5 ) =3 ( x+1 ) 2 ( x–1 ) +3 Dividiendo la ecuación para 3 ( x–2 ) 2 ( x+5 ) = ( x+1 ) 2 ( x–1 ) +1 ( x 2 –4x+4 ) ( x+5 ) =( x 2 +2x+1 ) ( x–1 ) +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