CAPITULO XXXI
R a d i c a l e s
Potenciación de radicales
R a d i c a l e s
Potenciación de radicales
- Ejercicio 245
Desarollar:
- ( 4 2 ) 2 = 4 2 2 2 =16 × 2 =32
- ( 2 3 ) 2 = 2 2 3 2 =4 × 3 =12
- ( 5 7 ) 2 = 5 2 7 2 =25 × 7 =175
- ( 2 43 ) 2 = 2 2 4 2 3 =4 2 4 3 =4 × 2 23 =8 23
- ( 3 2 a 2 b 3 ) 4 = 3 4 ( 2 a 2 b ) 4 3 =81 2 4 a 8 b 4 3 =81 × 2 a 2 b 2 a 2 b 3 =162 a 2 b 2 a 2 b 3
- ( 8 x 3 4 ) 2 = ( 2 3 x 3 ) 2 4 = 2 6 x 6 4 =2x ( 2x ) 2 =2x 2x
- ( 81a b 3 5 ) 3 = ( 9 2 a b 3 ) 3 5 = 9 6 a 3 b 9 5 =9b 9 a 3 b 4 5
- ( 186 ) 3 = 1 8 3 = 18 = 3 2 × 2 =3 2
- ( 4a 2x ) 2 = ( 4a ) 2 ( 2x ) 2 = 2 4 a 2 × 2x = 2 5 a 2 x =32 a 2 x
- ( 2 x+1 ) 2 = 2 2 ( x+1 ) 2 =4( x+1 ) =4x+4
- ( 3 x–a ) 2 = 3 2 ( x–a ) 2 =9( x–a ) =9x–9a
-
(
4
9
a
3
b
4
6
)
3
=
4
3
(
9
a
3
b
4
)
3
=
2
6
3
2
a
3
b
4
=
2
6
× 3a
b
2
a
=192a
b
2
a
Elevar al cuadrado: - 2 – 3 = ( 2 – 3 ) 2 =2–2 2 × 3 +3 =5–2 6
- 4 2 + 3 = ( 4 2 + 3 ) 2 = ( 4 2 ) 2 +8 2 × 3 +3 = 2 4 2+8 6 +3 = 2 5 +8 6 +3 =32+8 6 +3 =35+8 6
- 5 – 7 = ( 5 – 7 ) 2 =5–2 5 × 7 +7 =12–2 35
- 5 7 –6 = ( 5 7 –6 ) 2 = ( 5 7 ) 2 –2 × 5 7 × 6+36 =25 × 7–60 7 +36 =175–60 7 +36 =211–60 7
- x + x–1 = ( x + x–1 ) 2 = ( x ) 2 +2 x × x–1 + ( x–1 ) 2 =x+2 x 2 –x +x–1 =2x+2 x 2 –x –1
- x+1 –4 x = ( x+1 –4 x ) 2 = ( x+1 ) 2 –2 x+1 × 4 x + ( 4 x ) 2 =x+1–8 x 2 +x +16x =17x–8 x 2 +x +1
- a+1 – a–1 = ( a+1 – a–1 ) 2 = ( a+1 ) 2 –2 a+1 × a–1 + ( a–1 ) 2 =a+ 1 –2 a 2 –1 +a– 1 =2a–2 a 2 –1
- 2 2x–1 + 2x+1 = ( 2 2x–1 + 2x+1 ) 2 = ( 2 2x–1 ) 2 +2 × 2 2x–1 × 2x+1 + ( 2x+1 ) 2 =4( 2x–1 ) +4 4 x 2 –1 +2x+1 =8x–4+4 4 x 2 –1 +2x+1 =10x+4 4 x 2 –1 –3