Question

(radical din 5+2)totul la a doua-radical din 80

Answer 1

$\rm (2+\sqrt{5} )^2-\sqrt{80}=? \\ \\ (2+ \sqrt{5})^2=2^2+2\cdot2\cdot\sqrt{5}+( \sqrt{5} )^2 \\ \\ (2+ \sqrt{5})^2=4+4 \sqrt{5}+5=\bold{9+4\sqrt{5}} \\ \\ \sqrt{80}= \sqrt{16\cdot5}= \sqrt{4^2\cdot5}=\bold{4 \sqrt{5}} \\ \\ 9+\not4\sqrt\not5-\not4\sqrt\not5=\bold{9} \\ \\ \bold{R\v{a}spuns:9}$