Page 87 - E-Book SBMPTN Saintek

Bab 3

Bentuk Akar

A. Sifat-Sifat Bentuk Akar b ( a + b ) 2
• a + b = a + b × a + =
−
a. Bentuk Umum Akar a − b a − b a + b ab
m m
n m n m
a = a
a = a 2 C. Persamaan Bentuk Akar
1 1
n a = a n a = a 2
+
• (a b) 2 ab = a + b , syarat: a > b > 0
+
b. Penjumlahan dan Pengurangan Bukti:
1. ac + bc = (a b) c (a b) 2 ab
+
+
+
2. ac − bc = (a b) c = a + 2 ab + b
−
= a + ab + ab + b
c. Perkalian dan Pembagian
2 = ( a ) + ab + ab + ( b )
2
2
2
2
1. a ⋅ a = a = a = a
= a( a + b) + b( a + b)
n
n
2. a ⋅ n b = ab
= ( a + b)( a + b)
n m
3. a ⋅ n p n mp+ 2
a = a
= ( a + b ) = a + b
4. n p a = np a
s
a
• (a b) 2 ab = a − b,syarat a >t: a > b > 0
ar
y
+
−
b >
0

n a a
5. = n Bukti:
n b b
−
+
(a b) 2 ab
B. Merasionalkan Penyebut
= a 2 ab + b
−
a a b ab =
• = × = a − ab − ab + b
b b b b = 2 2
a a b ab ( a ) − ab − ab + ( b )
• = × =
b b b b = a( a − b) − b( a − b)
c c a − b
• = × =
a + b a + b a − b ( a − b)( a − b)
c( a − b) = ( a − b) = a − b
2
=
ab
−
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