Ta có:
12+√3+12−√312+3+12−3
=2−√3(2+√3)(2−√3)+2+√3(2−√3)(2+√3)=2−3(2+3)(2−3)+2+3(2−3)(2+3)
=2−√322−(√3)2+2+√322−(√3)2=2−322−(3)2+2+322−(3)2
=2−√34−3+2+√34−3=2−34−3+2+34−3
=2−√31+2+√31=2−31+2+31
=2−√3+2+√3=4=2−3+2+3=4.
Chọn đáp án (D). 44
Ta có : \(\frac{1}{2+\sqrt{3}}+\frac{1}{2-\sqrt{3}}=\frac{2-\sqrt{3}+2+\sqrt{3}}{4-3}=4\)
Vậy chọn D
\(\dfrac{1}{2+\sqrt{3}}+\dfrac{1}{2-\sqrt{3}}\)
=\(\dfrac{2-\sqrt{3}+2+\sqrt{3}}{\left(2-\sqrt{3}\right)\cdot\left(2+\sqrt{3}\right)}\)
=\(\dfrac{4}{4-3}\)
=\(\dfrac{4}{1}\)=4
⇒Chọn ý (D)
