Algebra Demystified 2nd Ed

Chapter 5 e X P O N e N T S a N D r O O T S 101

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 5

5. 2 1
   42

+ −

+

x =

()x

6.^6
211

1

()xx−+() 61 ()x^2

+

−

=

7.^4
3

9

2

1

xy^25 +−xy xy^33 =

✔SOLUTIONS

1.^62626262
xxyx

y

yxy

y

xy xy

y

xy

+=⋅+ =+= +

2.^31312233222
xy yxyy

xy

xy xy

xy

xy

xy

xy

−= −⋅ =−=−

3.^1
2

3

10

1

2

5

5

3

10

5

10

3

10

53

xx^22 x^22102

x

xx

x

xx

x

x

+=⋅+ =+= +

4.^11221111

2

x xyz xyzx^222

xyz

xyz xyz

x

xxyz

z

z

xyz

++=+⋅+ ⋅

=

22

22 22 22

2

xyz^22

x

xyz

z

xyz

xyz xz

xyz

++= ++

5. 2 1
   4

2

1

1

4

2

1

4

4

1

22

2

+ 2

−

+

=+ −

+

=⋅+

+

+ −

+

x

x

x

x

x

x

x

() () x

()

()( 44

24 1

4

2

2

2

)

()

()

= ++−

+

xx

x

6.^6
211

1

61

6

211

31

()()() ()^2 () 31

()

xx xxx ()

x

−+ x

+

−

=

−+

⋅ −

−

++

−

⋅ +

+

= −

−+

+ +

−

1

61

1

1

18 1

61 1

1

61

2

2

()

()

()()()

x

x

x

x

xx

x

x^22

2

1

18 11

61 1

()

()

()()

x

xx

xx

+

= −++

−+

7.

(^4)
3
9
2
14
3
2
2
9
2
3
3
1
2533 2
4
45
2
xy xy xy xy^2
xy
xy xy
y
y
+−=⋅+⋅−
xxy
x
x
xy
xy
y
xy
x
xy
xy
33
2
2
4
53
2
53
2
53
4
6
6
8
6
27
6
6
6
8
⋅
=+−=+^2276
6
22
53
yx
xy
−