Question

(b) If a= 5-2 √5, then find a²
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Answer 1

${(5 - 2 \sqrt{5} )}^{2} \\ 25 + 4 \times 5 - 2 \times 2 \times \sqrt{5} \times 5 \\ 25 + 20 - 4 \sqrt{5} \\ 45 - 4 \sqrt{5}$

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Answer 2

45 - 20√5

Step-by-step explanation:

$a = 5 - 2 \sqrt{5} \\ \\ {a}^{2} = (5 - 2 \sqrt{5} {)}^{2} \\ \\ = {5}^{2} - 2(5)( 2\sqrt{5} ) + ( {2 \sqrt{5}) }^{2} \\ \tiny\{( {a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} \} \\ \\ = > 25 - 20 \sqrt{5} + 20 \\ \\ = > 25 + 20 -20\sqrt{5} \\ \\ = > 45 - 20 \sqrt{5}$

Hence value of a² = 45 - 20√5

hope it helps.