Question

Aratati ca numarul $a = |2 \sqrt{3} - 5| - \frac{13}{2 \sqrt{3} +5 } }$ este rational

Answer 1

I2√3-5I=I5-2√3I=5-2√3
13/(2√3+5)=rationalizam=[13(2√3-5)/(12-5)]=(26√3-65)/7
a=5-2√3-(26√3-65)/7=(35-14√3-26√3+65)/7=(100-40√3)/7=20(5-2√3)/7