Teste 1B - Correcção Métodos Quantitativos I

1. a) b

2

a

8ab2

ba2

a4

ba2

ab16

ba2

ba4

ba2

a4ab16ba42

2

22

23

2

223

+−−=−

−+

−+

−=

−

−+

b) =−−=−⋅

−=−−=−− 222

22422

22

2222

2

128

2

132 235

22

32

2

41822

2

14 =⋅

−−=⋅

−−=

c) ( ) ( ) 4 34 354 2324 234 2 3 3 3 3 xyxyxyxyxyxyx ==⋅=⋅

d) ( ) ( ) ( ) =+−=+−=+− 3

233

132

123

2

3

1

2

1

3log4log5log27log64log25log27log3

264log

3

125log

2

1

4

45log

4

95log3log4log5log 2

=×

=+−=

2.

4x3 –5x

2 +3x –2 x + 1

4x3 +4x

2 4x

2 – 9x +12

–9x2 +3x

–9x2 –9x

12x –2

12x +12

–14

3. a) ( ) ( )( )

1612943

443343

43

43

43

43

43

6427 2222333333

++=−

+⋅+−=

−

−=

−

−=

−

−xx

x

xxx

x

x

x

x

x

x

b) ( )( )( )( ) 2

5

21

51

2

562

2

+

−=

+−

−−=

−+

+−

x

x

xx

xx

xx

xx

c) ( ) ( ) ( ) ( )( ) ( ) ( )( ) ( )( )yxyxyxyxyxyxyxyx 925873257325732522

+−=−−+⋅−++=−−+

d) ( ) ( )( ) ( )( )

=−+

+++

−+

=−−

+++

−+ 2121

3

22

5

223

3

42

522

xx

x

xxxxx

x

xxx

( )( ) ( ) ( )( )( )( )

( ) ( ) ( )( )( )( )

=−++

++−−−−=

−++

++−−−+=

2212

421261055

2212

2226215 22

xxx

xxxxx

xxx

xxxxx

( )( )( )2212

277 2

−++

+−=

xxx

xx

1

141294

1

2354 223

+−+−=

+

−+−

xxx

x

xxx

4. a) ( ) ( ) 202044442242

2

4 222=⇒=−⇒=+−⇒=−⇒×=−⇒=

−xxxxxxxx

x

x

b)

( )( )( )

⇒−=−

⇒−=−

−−⇒−=

−

−

−

⇒−=−

+−32

3

1

232

3

12

21232

3

12

22

12

32

3

12

252 2

xx

xx

xxx

x

xx

xx

xx

( ) 332633223 =⇒−=−⇒−=−⇒ xxxxx

c)

( )( ) ( )( )( )( )

( ) ( )( )( )

( )( ) ( )( )( ) ( )

⇒−=++−

−−−++⇒−=

−+

++−

+−

−−−++

⇒−=

−+

+

+

−−

−

+

211

11112

11

11

11

1111

2

1

1

1

11

1

1

1

xxx

xxxxx

xx

xx

xx

xxxx

x

xx

x

x

x

x

( ) ( )4222

2

42

2

1212 22

=⇒−=⇒−=⇒−=+−−++

⇒ xxxx

xx

x

xxxx