Ejercicio 143

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CAPITULO XVI

Ecuaciones literales de primer grado con una icognita
Ejercicio 143
Resolver las siguientes ecuaciones:
  1. a(x+1 ) =1 x+1 = 1 a x = 1 a 1 x = 1a a
  2. ax4 =bx2 axbx =42 x(ab ) =2 x = 2 ab
  3. ax+ b 2 = a 2 bx axbx = a 2 b 2 x (ab ) =(a+b )(ab ) x =a+b
  4. 3(2ax ) +ax = a 2 +9 6a3x+ax = a 2 +9 x(a3 ) = a 2 6a+9 x = (a3 ) 2 (a3 ) x =a3
  5. a(x+b ) +x(ba ) =2b(2ax ) ax +ab+bx ax =4ab2bx bx+2bx =4abab 3b x = 3 a b x =a
  6. (xa ) 2 (x+a ) 2 =a(a7x ) [(xa ) +(x+a ) ] [(xa ) (x+a ) ] = a 2 7ax (x a +x+ a ) ( x a x a ) = a 2 7ax 2x(2a ) +7ax = a 2 4ax+7ax = a 2 3ax = a 2 x = a 2 3 a x = a 3
  7. axa(a+b ) =x(1+ab ) ax+x =a(a+b ) 1ab x(a+1 ) = a 2 + ab 1 ab x(a+1 ) = a 2 1 x (a+1 ) = (a+1 )(a1 ) x =a1
  8. a 2 (ax ) b 2 (xb ) = b 2 (xb ) a 2 (ax ) b 2 (xb ) b 2 (xb ) =0 a 2 (ax ) 2 b 2 (xb ) =0 a 3 a 2 x2 b 2 x+2 b 3 =0 a 3 +2 b 3 = a 2 x+2 b 2 x a 3 +2 b 3 =x( a 2 +2 b 2 ) x = a 3 +2 b 3 a 2 +2 b 2
  9. (x+a ) (xb ) (x+b ) (x2a ) =b(a2 ) +3a x 2 bx+axab( x 2 2ax+bx2ab ) =ab2b+3a x 2 bx+axab x 2 +2axbx+2ab =ab2b+3a 3ax2bx+ ab = ab 2b+3a x (3a2b ) = 3a2b x =1
  10. x 2 + a 2 = (a+x ) 2 a(a1 ) x 2 + a 2 = a 2 +2ax+ x 2 a 2 +a a 2 a =2ax a(a1 ) =2ax a (a1 ) 2 a =x x = a1 2
  11. m(nx ) m(n1 ) =m(mxa ) m [(nx ) (n1 ) ] = m (mxa ) n x n +1 =mxa a+1 =mx+x a+1 =x(m+1 ) x = a+1 m+1
  12. xa+2 =2ax3(a+x ) 2(a5 ) xa+2 =2ax3a3x2a+10 x2ax+3x =5a+a+102 4x2ax =84a 2 x (2a ) = (2a ) x =2
  13. a(xa ) 2bx =b(b2ax ) ax a 2 2bx = b 2 2abbx ax2bx+bx = a 2 2ab+ b 2 axbx = (ab ) 2 x(ab ) = (ab ) 2 x = (ab ) 2 ab x =ab
  14. ax+bx = (x+ab ) 2 (x2b ) (x+2a ) ax+bx = x 2 +2ax+ a 2 2ab2bx+ b 2 ( x 2 +2ax2bx4ab ) ax+bx = x 2 + 2ax + a 2 2ab 2bx + b 2 x 2 2ax + 2bx +4ab x(a+b ) = a 2 +2ab+ b 2 x = (a+b ) 2 a+b x =a+b
  15. x(a+b ) 3a(a2 ) =2(x1 ) x(ab ) x(a+b ) 2(x1 ) +x(ab ) =3+a(a2 ) ax+ bx 2x+2+ax bx =3+ a 2 2a 2ax2x = a 2 2a+32 2x(a1 ) = (a1 ) 2 x = (a1 ) 2 2 (a1 ) x = a1 2
  16. (m+4x ) (3m+x ) = (2xm ) 2 +m(15xm ) 3 m 2 +mx+12mx+ 4 x 2 = 4 x 2 4mx+ m 2 +15mx m 2 3 m 2 +13mx =11mx 13mx11mx =3 m 2 2mx =3 m 2 x = 3 m 2 2 m x = 3m 2
  17. a 2 (ax ) a 2 (a+1 ) b 2 (bx ) b(1 b 2 ) +a(1+a ) =0 a 2 (ax ) b 2 (bx ) = a 2 (a+1 ) a(1+a ) +b(1 b 2 ) a 3 a 2 x b 3 + b 2 x =a(a+1 ) [a1 ] +b b 3 a 3 a 2 x+ b 2 x =a( a 2 1 ) +b a 3 +( b 2 a 2 ) x = a 3 a+b x = ba b 2 a 2 x = ba (b+a )(ba ) x = 1 a+b
  18. (axb ) 2 =(bxa ) (a+x ) x 2 (b a 2 ) + a 2 +b(12b ) (axb ) 2 (bxa ) (a+x ) + x 2 (b a 2 ) = a 2 +b(12b ) a 2 x 2 2abx+ b 2 abx b x 2 + a 2 +ax+ b x 2 a 2 x 2 = a 2 +b2 b 2 3abx+ax =b2 b 2 b 2 ax (13b ) =b (13b ) x = b a
  19. (x+b ) 2 (xa ) 2 (a+b ) 2 =0 (x+b ) 2 (xa ) 2 = (a+b ) 2 [(x+b ) +(xa ) ] [(x+b ) (xa ) ] = (a+b ) 2 (x+b+xa ) ( x +b x +a ) = (a+b ) 2 (2x+ba )(a+b ) = (a+b ) 2 2x+ b a =a+ b 2x =a+a 2 x = 2 a x =a
  20. (x+m ) 3 12 m 3 = (xm ) 3 +2 x 3 (x+m ) 3 + (xm ) 3 =2 x 3 +12 m 3 [(x+m ) +(xm ) ] [ (x+m ) 2 (x+m ) (xm ) + (xm ) 2 ] =2( x 3 +6 m 3 ) (x+ m +x m ) [ x 2 + 2mx + m 2 ( x 2 m 2 ) + x 2 2mx + m 2 ] =2( x 3 +6 m 3 ) 2 x[2 x 2 +2 m 2 x 2 + m 2 ] = 2 ( x 3 +6 m 3 ) x( x 2 +3 m 2 ) = x 3 +6 m 3 x 3 +3x m 2 = x 3 +6 m 3 x = m 3 3 m 2 x =2m