algebra-manual-de-preparacion-preuniversitaria-219

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sustituyendo en E:
____ __ __ ___
√6ny √2 √3 √ny 
E = –––––––– = ––––––––––––__ ___ __ ___
√2 √ny √2 √ny
__
E = √3
6.- Efectuar:
____ ____ ____
√a - b + √b - c + √c - a 
E = –––––––––––––––––––––––––––––––––––––––__________ __________ _________
1/2
[√(a - b)(b - c) + √(a - b)(c - a) + √(b - c)(c - a)]
Solución:
Elevando al cuadrado la expresión:
____ ____ ____
2
(√a - b + √b - c + √c - a )
E = –––––––––––––––––––––––––––––––––––––––__________ __________ _________
√(a - b)(b - c) + √(a - b)(c - a) + √(b - c)(c - a)
efectuando operaciones:
_________ _________
a -b + b - c+c - a+2√(a -b)(b - c) + 2√(a -b)(b - c)
E2 = ––––––––––––––––––––––––––––––––––––––__________ __________ _________
√(a - b)(b - c) + √(a - b)(c - a) + √(b - c)(c - a)
_________
+ 2√(b - c)(c - a)
––––––––––––––––
reduciendo y factorizando:
__________ __________ __________
2[√(a - b)(b - c)+ √(a - b)(c - a)+ √(b - c)(c - a)]
E2 = ––––––––––––––––––––––––––––––––––––––__________ __________ __________
[√(a - b)(b - c)+ √(a - b)(c - a)+ √(b - c)(c - a)]
simplificando: E2 = 2
__
∴ E = √2 
7.- Simplificar:
3 3__ ____
2
__
2
(4 + √15 ) + (4 - √15)
E = –––––––––––––––––––––––––––
3 3__ ____
2
__
2
(6 + √35 ) - (6 - √35)
Solución:
Multiplicando y dividiendo por (2)3/2 se obtiene:
3 3__ ____
2
__
2
(8 + 2√15 ) + (8 - 2√15)
E = –––––––––––––––––––––––––––––
3 3__ ____
2
__
2
(12 + 2√35 ) - (12 - 2√35)
__ 3 __ 3
(8 + 2√15 ) + (8 - 2√15)
E = –––––––––––––––––––––––––––––__ 3 __ 3
(12 + 2√35 ) - (12 - 2√35)
transformando los radicales dobles a simples:
__ __ 3 __ __ 3
(√5 + √3 ) + (√5 - √3 ) 
E = ––––––––––––––––––––––––––––––––__ __ 3 __ __ 3
(√7 + √5 ) - (√7 - √5 ) 
elevando al cubo:
__ 3 __ 2 __ __ __ 2 __ 3
(√5 ) + 3(√5 )(√3 )+3(√5 )(√3 )+(√3 )
E = ––––––––––––––––––––––––––––––––––––__ 3 __ 2 __ __ __ 2 __ 3
(√7 ) + 3(√7 )(√5 )+3(√7 )(√5 )+(√5 )
__ 3 __ 2 __ __ __ 2 __ 3
+ (√5 ) - 3(√5 )(√3 )+3(√5 )(√3 )+(√3 )
––––––––––––––––––––––––––––––––––––––__ 3 __ 2 __ __ __ 2 __ 3
- (√7 ) + 3(√7 )(√5 )- 3(√7 )(√5 )+(√5 )
reduciendo:
__ 3 __ __ 2
2(√5 ) + 6(√5 )(√3 ) 
E = –––––––––––––––––––––––__ 2 __ __ 3
6(√7 )(√5 ) + 2(√5 ) 
factorizando:
__ __ 2 __ 2
2(√5 )[(√5 ) + 3(√3 ) ]
E = ––––––––––––––––––––––––––__ __ 2 __ 2
2(√5 )[3(√7 ) + (√5 ) ]
5 + 9 14 7 E = –––––– = ––– = –––
21 + 5 26 13
8.- Efectuar:
__________ _____________ ____
√26 + √675 - √26 - √675 
E = ––––––––––––––––––––––––––––____________ ______________ ____
3√26 + √675 + 3√26 - √675
Solución:
Trabajando separadamente el numerador y
denominador:
___________ _____________ ___
N = √26 + √675 - √26 - √675 
elevando al cuadrado:
______________ ___ 2 ___
N2 = 26 + √675 - 2 √262-( √675) + 26 - √675
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Algebra 27/7/05 16:30 Página 231