Question

Racionalize os denominadores das expressões a seguir:
(VALENDO 50 PONTOS)

Answer 1

Resposta:

Explicação passo-a-passo:

.

e)..(2 - 2√2) / (2 - √2) =

(2 + √2).(2 - 2√2) / (2 + √2).(2 - √2) =

(4 - 4√2 + 2√2 - 2√4) / (2² - √2²) =

(4 - 2√2 - 2 . 2) / (4 - 2) =

(4 - 4 - 2√2) / 2 =

- 2√2 / 2 =

- √2

.

f)..(√3 - √2) / (√3 + √2) =

... (√3 - √2).(√3 - √2)/(√3-√2).(√3+√2)

..= (√9 - √6 - √6 + √4) / (√9 - √4)

..= ( 3 - 2.√6 + 2) / (3 - 2)

..= 5 - 2√6 / 1

..= 5 - 2√6

.

(Espero ter colaborado)

Answer 2

Oie, Td Bom?!

e)

$= \frac{2 - 2 \sqrt{2} }{2 - \sqrt{2} } \\ = \frac{ \sqrt{2} \: . \: ( \sqrt{2} - 2) }{ - ( \sqrt{2} - 2)} \\ = \sqrt{2} \: . \: ( - 1) \\ = - \sqrt{2} \: . \: 1 \\ = - \sqrt{2}$

f)

$=\frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ =\frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \: . \: \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ = \frac{( \sqrt{3} - \sqrt{2} ) \: . \: ( \sqrt{3} - \sqrt{2} ) }{( \sqrt{3} + \sqrt{2} ) \: . \: ( \sqrt{3} - \sqrt{2} )} \\= \frac{( \sqrt{3} - \sqrt{2} ) \: . \: ( \sqrt{3} - \sqrt{2} )}{3 - 2} \\ =\frac{( \sqrt{3} - \sqrt{2}) \: . \: ( \sqrt{3} - \sqrt{2} )}{1} \\= ( \sqrt{3} - \sqrt{2} ) \: . \: ( \sqrt{3} - \sqrt{2} ) \\= ( \sqrt{3} - \sqrt{2} ) {}^{2} \\= 3 - 2 \sqrt{6} + 2 \\= 5 - 2 \sqrt{6}$

Att. Makaveli1996