Ejercicio 144

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CAPITULO XVI

Ecuaciones literales de primer grado con una icognita
Ejercicio 144
Resolver las siguientes ecuaciones:
  1. m x 1 m = 2 m m 2 x m x = 2 m m 2 x =2x m 2 =2x+x m 2 =3x x = m 2 3
  2. a x + b 2 = 4a x 2a+bx 2 x = 4a x 2a+bx =8a bx =8a2a bx =6a x = 6a b
  3. x 2a 1x a 2 = 1 2a ax1+x 2 a 2 = 1 2a ax1+x =a x (a+1 ) = a+1 x =1
  4. m x + n m = n x +1 m 2 +nx m x = n+x x m 2 +nx =m(n+x ) m 2 +nx =mn+mx m 2 mn =mxnx m (mn ) =x (mn ) x =m
  5. a1 a + 1 2 = 3a2 x 2(a1 ) +a 2a = 3a2 x 2a2+a 2a = 3a2 x 3a2 2a = 3a2 x x (3a2 ) =2a (3a2 ) x =2a
  6. ax a bx b = 2(ab ) ab b(ax ) a(bx ) ab = 2(ab ) ab ab bx ab +ax =2(ab ) x (ab ) =2 (ab ) x =2
  7. x3a a 2 2ax ab = 1 a b(x3a ) a(2ax ) a 2 b = 1 a bx3ab2 a 2 +ax =ab ax+bx =2 a 2 +3abab ax+bx =2 a 2 +2ab x (a+b ) =2a (a+b )
  8. x+m m x+n n = m 2 + n 2 mn 2 n(x+m ) m(x+n ) mn = m 2 + n 2 2mn mn nx+ mn mx mn = n 2 2mn+ m 2 x (nm ) = (nm ) 2 x =nm
  9. xb a =2 xa b xb a + xa b =2 b(xb ) +a(xa ) ab =2 bx b 2 +ax a 2 =2ab ax+bx = a 2 +2ab+ b 2 x (a+b ) = (a+b ) 2 x =a+b
  10. 4x 2a+b 3 = 3 2 4x 2a+b =3 3 2 4x 2a+b = 63 2 4x 2a+b = 3 2 2(4x ) =3(2a+b ) 8x =3(2a+b ) x = 3(2a+b ) 8
  11. 2a+3x x+a = 2(6xa ) 4x+a 2a+3x x+a = 12x2a 4x+a (2a+3x ) (4x+a ) =(12x2a ) (x+a ) 8ax+2 a 2 + 12 x 2 +3ax = 12 x 2 +12ax2ax2 a 2 2 a 2 +2 a 2 =10ax11ax 4 a 2 = a x x =4a
  12. 2(xc ) 4xb = 2x+c 4(xb ) 2x2c 4xb = 2x+c 4x4b (2x2c ) (4x4b ) =(2x+c ) (4xb ) 8 x 2 8bx8cx+8bc = 8 x 2 2bx+4cxbc 8bx8cx4cx+2bx =8bcbc 6bx12cx =9bc x(b+c ) =bc x = 3bc 2(b+c )
  13. 1 n m x = 1 mn 1 x xmn nx = xmn m nx m(xmn ) =xmn mx m 2 n =xmn mxx = m 2 nmn x (m1 ) =mn (m1 ) x =mn
  14. (x2b ) (2x+a ) (xa ) (a2b+x ) =2 (x2b ) (2x+a ) =2(xa ) (a2b+x ) 2 x 2 +ax4bx2ab =2( ax 2bx+ x 2 a 2 +2ab ax ) 2 x 2 +ax 4bx 2ab = 4bx + 2 x 2 2 a 2 +4ab ax =2ab2 a 2 +4ab ax =6ab2 a 2 a x =2 a (3ba ) x =2(3ba )
  15. x+m xn = n+x m+x (x+m ) (m+x ) =(n+x ) (xn ) (x+m ) 2 = x 2 n 2 x 2 +2mx+ m 2 = x 2 n 2 2mx = m 2 n 2 x = m 2 + n 2 2m
  16. x(2x+3b ) (x+b ) x+3b =2 x 2 bx+ b 2 x(2 x 2 +3bx+2bx+3 b 2 ) =(x+3b ) (2 x 2 bx+ b 2 ) 2 x 3 + 5b x 2 +3 b 2 x = 2 x 3 b x 2 + b 2 x+ 6b x 2 3 b 2 x+3 b 3 3 b 2 x+2 b 2 x =3 b 3 5 b 2 x =3 b 3 x = 3b 5
  17. 3 4 ( x b + x a ) = 1 3 ( x b x a ) + 5a+13b 12a 3 4 ( ax+bx ab ) = 1 3 [ x b x a + 5a+13b 4a ] 3 4 ( ax+bx ab ) = 1 3 [ 4ax4bx+5ab+13 b 2 4 ab ] 9(ax+bx ) =4ax4bx+5ab+13 b 2 9ax+9bx4ax+4bx =5ab+13 b 2 5ax+13bx =b(5a+13b ) x (5a+13b ) =b (5a+13b ) x =b
  18. x+a 3 = (xb ) 2 3xa + 3ab3 b 2 9x3a x+a 3 = (xb ) 2 3xa + 3 (ab b 2 ) 3 (3xa ) x+a 3 = 1 3xa [ (xb ) 2 +ab b 2 ] x+a 3 = 1 3xa [ x 2 2bx+ b 2 +ab b 2 ] (x+a ) (3xa ) =3( x 2 2bx+ab ) 3 x 2 ax+3ax a 2 = 3 x 2 6bx+3ab 2ax+6bx = a 2 +3ab 2x (a+3b ) =a (a+3b ) x = a 2
  19. 5x+a 3x+b = 5xb 3xa (5x+a ) (3xa ) =(5xb ) (3x+b ) 15 x 2 5ax+3ax a 2 = 15 x 2 +5bx3bx b 2 5ax+3ax5bx+3bx = a 2 b 2 2ax2bx =(ab ) (a+b ) 2x (a+b ) =(ab )(a+b ) x = ba 2
  20. x+a xa xa x+a = a(2x+ab ) x 2 a 2 (x+a ) 2 (xa ) 2 (xa ) (x+a ) = a(2x+ab ) x 2 a 2 [(x+a ) +(xa ) ] [(x+a ) (xa ) ] =2ax+ a 2 b (x+ a +x a ) ( x +a x +a ) =2ax+ a 2 b 2x(2a ) =2ax+ a 2 b 4ax2ax = a 2 b 2 a x = a 2 b x = ab 2
  21. 2x3a x+4a 2 = 11a x 2 16 a 2 2x3a2(x+4a ) x+4a = 11a (x+4a )(x4a ) 2x 3a 2x 8a = 11a x4a 11a (x4a ) = 11a x+4a =1 x =4a1
  22. 1 x+a + x 2 a 2 +ax = x+a a 1 x+a + x 2 a(x+a ) = x+a a 1 x+a (1+ x 2 a ) = x+a a 1 x+a ( a+ x 2 a ) = x+a a a+ x 2 = (x+a ) 2 a+ x 2 = x 2 +2ax+ a 2 a a 2 =2ax a (1a ) =2 a x x = 1a 2
  23. 2(a+x ) b 3(b+x ) a = 6( a 2 2 b 2 ) ab 2a(a+x ) 3b(b+x ) ab = 6( a 2 2 b 2 ) ab 2 a 2 +2ax3 b 2 3bx =6 a 2 12 b 2 2ax3bx =6 a 2 2 a 2 12 b 2 +3 b 2 x(2a3b ) =4 a 2 9 b 2 x (2a3b ) =(2a+3b )(2a3b ) x =2a+3b
  24. m(nx ) (mn ) (m+x ) = n 2 1 n (2m n 2 3 m 2 n ) mnmx( m 2 +mxmnnx ) = n 2 1 n n (2mn3 m 2 ) mn mx m 2 mx+ mn +nx = n 2 2mn+3 m 2 nx2mx = n 2 2mn+3 m 2 + m 2 x(n2m ) = n 2 2mn+4 m 2 x (n2m ) = (n2m ) 2 x =n2m