Page 11 - ALGEBRA 1RO SECUNDARIA

Álgebra 1° Secundaria

PROBLEMAS RESUELTOS

4
8
2
2
1. Efectúe: (m + 3)(m – 3)(m + 9) – m

A) 81 B) –81 C) 12m D) 9 E) –9

Resolución
2
2
4
8
( ( m 2 ) − ( ) )( m + ) 9 − m
3
4
8
4
( m − 9 )( m + 9 ) − m
8
( m 4 ) − 2 ( ) 9 2 − m
−
8
8
m − 81 m = − 81
Rpta.: B

1
2. Si x + = 3
x
1
3
Halle: x +
x 3

A) 27 B) 25 C) 20 D) 18 E) 16

Resolución
 1 3 = ( )
3
3
 x +  x  
3
1


1
( ) x 3 +   + 3 ( ) x   x + 1  = 27
 x   x  x 
1
( )( ) =
3
x + + 3 1 3 27
x 3
1
3
x + = 27 9
−
x 3
1
3
x +
3
x = 18
Rpta.: D

2
2
2
3. Efectuar: (m + 4m + 7)(m + 4m – 1) – (m + 4m + 3)
2

A) –16 B) 116 C) –9 D) 9 E) 0

Resolución
m + 4m = x
2
(x + 7)(x – 1) – (x + 3)
2
2
x + (7 + –1) x + (7)(–1) – (x + 3)
2
2
2
2
x + 6x – 7 – ((x) + 2(x)(3) + (3) )
2
x + 6x – 7 – (x + 6x + 9)
2
2
2
x + 6x – 7 – x – 6x – 9
–7 –9 = –16
Rpta.: a

2
4. Efectúe: (m + n – 2)(m – n + 2) + (n – 2)

A) 1 B) m C) m 2 D) n 2 E) 2mn

Resolución
(m + (n – 2))(m – (n – 2)) + (n – 2) 2
2
2
2
= (m) – (n – 2) + (n – 2)
= m
2
Rpta.: C

5. Efectúe: (m + n) + (m – n)
3
3

A) 18 B) 18 m C) 18 n D) 18 m n E) 18 mn
2
2

Resolución
3
3
m + 3m n + 3mn + n +
2
2
3
2
3
2
m − 3m n + 3mn − n +
− 2m 3 12mn 2
18mn 2
Rpta.: E
er
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