Question

Calculați:
1) (3 - radical din 3 - radical din 5)^2

Answer 1

${(3 - \sqrt{3} - \sqrt{5} )}^{2} = {3}^{2} + {( \sqrt{3} )}^{2} + {( \sqrt{5} )}^{2} - 2 \times 3 \times \sqrt{3} + 2 \times \sqrt{3} \times \sqrt{5} - 2 \times 3 \times \sqrt{5}$

$= 9 + 3 + 5 - 6 \sqrt{3} + 2 \sqrt{15} - 6 \sqrt{5}$

$= 17 - 6 \sqrt{3} + 2 \sqrt{15} - 6 \sqrt{5}$

${(a-b-c)}^{2}={a}^{2}+{b}^{2}+{c}^{2}-2ab+2bc-2ac$

Answer 2

(3-√3-√5)^2=
fie a=3-√3
(a-√5)^2=a^2-2√5a+5
inlocuind
(3-√3)^2-2√5(3-√3)+5=
9-6√3+3-6√5+2√15+5=
17-6√3-6√5+2√15