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\(\frac {2} {\sqrt 3 \,-\, 1} = \)
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A. 1 +  |
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| B. 2 |
| C. 2 + |
| D. 2 . |
| E. 2,5 |
[ 4-3208 - op net sinds 13.12.01-(E)-24.10.2023 ]
Translation in E N G L I S H
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\(\frac {2} {\sqrt 3 \: - \: 1} = \)
|
A. 1 + |
|---|
| B. 2 |
| C. 2 + |
| D. 2 . |
| E. 2.5 |
Oplossing - Solution
1ste manier :
\(
\frac {2} {\sqrt 3 - 1} = \frac {2.(\sqrt 3 + 1)} {(\sqrt 3 - 1)((\sqrt 3 + 1))}=\frac {2.(\sqrt 3 + 1)} {3-1}=\sqrt 3 + 1
\)
2de manier :
Je kan direct zien dat A het juiste antwoord is.
Waarom is \(\frac {33} {3} \) = 11 ? Omdat 3.11 = 33
Waarom is \( \frac {2} {\sqrt 3 - 1} = \sqrt 3 + 1 \;? \)
Omdat \((\sqrt 3 - 1).(\sqrt 3 - 1) \) = 2.
Immers \((\sqrt 3 - 1).(\sqrt 3 - 1) = 3 - 1 = 2 \)
