\(\left ( 2^{2-\sqrt 3} - 2^{-\sqrt 3} \right )^2\)
is gelijk aan
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A. 9 . 2−2√3 |
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| B. 24−2√3 − 2−2√3 |
| C. 4 . 2−√3 − 2−2√3 |
| D. 16.2−2√3 − 24−2√3 + 2−2√3 |
| E. 16.2−2√3 − 8.2−2√3 + 2−2√3 |
[ 6-2613 - op net sinds 30.3.2020-(E)-16.10.2026 ]
Translation in E N G L I S H
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\(\left ( 2^{2-\sqrt 3} - 2^{-\sqrt 3} \right )^2=\)
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Oplossing - Solution
\(\left ( 2^{2-\sqrt 3} - 2^{-\sqrt 3} \right )^2= 2^{4-2\sqrt 3} + 2^{-2\sqrt 3}-2.2^{2-\sqrt 3}.2^{-\sqrt 3}\\ =16.2^{-2\sqrt 3} + 2^{-2\sqrt 3}-2^{3-2\sqrt 3}\\ =16.2^{-2\sqrt 3} + 2^{-2\sqrt 3}-8.2^{-2\sqrt 3}\\ =9.2^{-2\sqrt 3}\)
(16 + 1 − 8 = 9)