Comparte esto 👍👍DESCARGACAPITULO XVI Ecuaciones literales de primer grado con una icognitaEjercicio 143Resolver las siguientes ecuaciones: a(x+1 ) =1 x+1 = 1 a x = 1 a –1 x = 1–a a ax–4 =bx–2 ax–bx =4–2 x(a–b ) =2 x = 2 a–b ax+ b 2 = a 2 –bx ax–bx = a 2 – b 2 x (a–b ) =(a+b )(a–b ) x =a+b 3(2a–x ) +ax = a 2 +9 6a–3x+ax = a 2 +9 x(a–3 ) = a 2 –6a+9 x = (a–3 ) 2 (a–3 ) x =a–3 a(x+b ) +x(b–a ) =2b(2a–x ) ax +ab+bx– ax =4ab–2bx bx+2bx =4ab–ab 3b x = 3 a b x =a (x–a ) 2 – (x+a ) 2 =a(a–7x ) [(x–a ) +(x+a ) ] [(x–a ) –(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 ax–a(a+b ) =–x–(1+ab ) ax+x =a(a+b ) –1–ab x(a+1 ) = a 2 + ab –1– ab x(a+1 ) = a 2 –1 x (a+1 ) = (a+1 )(a–1 ) x =a–1 a 2 (a–x ) – b 2 (x–b ) = b 2 (x–b ) a 2 (a–x ) – b 2 (x–b ) – b 2 (x–b ) =0 a 2 (a–x ) –2 b 2 (x–b ) =0 a 3 – a 2 x–2 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 (x+a ) (x–b ) –(x+b ) (x–2a ) =b(a–2 ) +3a x 2 –bx+ax–ab–( x 2 –2ax+bx–2ab ) =ab–2b+3a x 2 –bx+ax–ab– x 2 +2ax–bx+2ab =ab–2b+3a 3ax–2bx+ ab = ab –2b+3a x (3a–2b ) = 3a–2b x =1 x 2 + a 2 = (a+x ) 2 –a(a–1 ) x 2 + a 2 = a 2 +2ax+ x 2 – a 2 +a a 2 –a =2ax a(a–1 ) =2ax a (a–1 ) 2 a =x x = a–1 2 m(n–x ) –m(n–1 ) =m(mx–a ) m [(n–x ) –(n–1 ) ] = m (mx–a ) n –x– n +1 =mx–a a+1 =mx+x a+1 =x(m+1 ) x = a+1 m+1 x–a+2 =2ax–3(a+x ) –2(a–5 ) x–a+2 =2ax–3a–3x–2a+10 x–2ax+3x =–5a+a+10–2 4x–2ax =8–4a 2 x (2–a ) = (2–a ) x =2 a(x–a ) –2bx =b(b–2a–x ) ax– a 2 –2bx = b 2 –2ab–bx ax–2bx+bx = a 2 –2ab+ b 2 ax–bx = (a–b ) 2 x(a–b ) = (a–b ) 2 x = (a–b ) 2 a–b x =a–b ax+bx = (x+a–b ) 2 –(x–2b ) (x+2a ) ax+bx = x 2 +2ax+ a 2 –2ab–2bx+ b 2 –( x 2 +2ax–2bx–4ab ) 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 x(a+b ) –3–a(a–2 ) =2(x–1 ) –x(a–b ) x(a+b ) –2(x–1 ) +x(a–b ) =3+a(a–2 ) ax+ bx –2x+2+ax– bx =3+ a 2 –2a 2ax–2x = a 2 –2a+3–2 2x(a–1 ) = (a–1 ) 2 x = (a–1 ) 2 2 (a–1 ) x = a–1 2 (m+4x ) (3m+x ) = (2x–m ) 2 +m(15x–m ) 3 m 2 +mx+12mx+ 4 x 2 = 4 x 2 –4mx+ m 2 +15mx– m 2 3 m 2 +13mx =11mx 13mx–11mx =–3 m 2 2mx =–3 m 2 x =– 3 m 2 2 m x =– 3m 2 a 2 (a–x ) – a 2 (a+1 ) – b 2 (b–x ) –b(1– b 2 ) +a(1+a ) =0 a 2 (a–x ) – b 2 (b–x ) = a 2 (a+1 ) –a(1+a ) +b(1– b 2 ) a 3 – a 2 x– b 3 + b 2 x =a(a+1 ) [a–1 ] +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 = b–a b 2 – a 2 x = b–a (b+a )(b–a ) x = 1 a+b (ax–b ) 2 =(bx–a ) (a+x ) – x 2 (b– a 2 ) + a 2 +b(1–2b ) (ax–b ) 2 –(bx–a ) (a+x ) + x 2 (b– a 2 ) = a 2 +b(1–2b ) a 2 x 2 –2abx+ b 2 –abx– b x 2 + a 2 +ax+ b x 2 – a 2 x 2 = a 2 +b–2 b 2 –3abx+ax =b–2 b 2 – b 2 ax (1–3b ) =b (1–3b ) x = b a (x+b ) 2 – (x–a ) 2 – (a+b ) 2 =0 (x+b ) 2 – (x–a ) 2 = (a+b ) 2 [(x+b ) +(x–a ) ] [(x+b ) –(x–a ) ] = (a+b ) 2 (x+b+x–a ) ( x +b– x +a ) = (a+b ) 2 (2x+b–a )(a+b ) = (a+b ) 2 2x+ b –a =a+ b 2x =a+a 2 x = 2 a x =a (x+m ) 3 –12 m 3 =– (x–m ) 3 +2 x 3 (x+m ) 3 + (x–m ) 3 =2 x 3 +12 m 3 [(x+m ) +(x–m ) ] [ (x+m ) 2 –(x+m ) (x–m ) + (x–m ) 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 Categories: Capítulo XVI