Ta có: 4>3⇒√4>√3⇒2>√3>04>3⇒4>3⇒2>3>0
Suy ra: √2+√3+√2−√3>02+3+2−3>0
Ta có:
(√2+√3+√2−√3)2(2+3+2−3)2=2+√3+2√2+√3.√2−√3+2−√3=2+3+22+3.2−3+2−3
=4+2√4−3=4+2√1=4+2=6=4+24−3=4+21=4+2=6
(√6)2=6(6)2=6
Vì (√2+√3+√2−√3)2=(√6)2(2+3+2−3)2=(6)2 nên √2+√3+√2−√3=√6
Chuc ban hoc tot.