Question

$\sqrt{21-12 \sqrt{3} }$

Answer 1

O idee elementara!

21 - 12$\sqrt{3}$ = $( a - b)^{2}$ = $a^{2} + b^{2} -2ab$ <=>
21 = $a^{2} + b^{2}$ si [tex]12 \sqrt{3} = 2ab => ab = 6 \sqrt{3} ; [/tex]
=> a = $2 \sqrt{3}$ si b = 3 => 21 - 12$\sqrt{3}$ = $(2 \sqrt{3}-3 )^{2}$ => $\sqrt{21-12 \sqrt{3} }$ = /$2 \sqrt{3} -3$/ = $2 \sqrt{3} -3$ pt. ca $2 \sqrt{3} > 3$;
Bafta!