Question

Rút gọn: \(D=\sqrt{\frac{8+\sqrt{15}}{2}}+\sqrt{\frac{8-\sqrt{15}}{2}}\)

Answer 1

\(D=\sqrt{\frac{8+\sqrt{15}}{2}}+\sqrt{\frac{8-\sqrt{15}}{2}}\)

\(\Rightarrow D^2=\frac{8+\sqrt{15}}{2}+\frac{8-\sqrt{15}}{2}+2.\sqrt{\frac{\left(8+\sqrt{15}\right)\left(8-\sqrt{15}\right)}{2.2}}\)

\(=8+2.\sqrt{\frac{64-15}{4}}\)

\(=8+2.\frac{7}{2}=8+7=15\)

\(\Rightarrow D=\sqrt{15}\text{ Hoặc }D=-\sqrt{15}\)

\(\text{Mà }D>0\text{ nên }D=\sqrt{15}\)

Answer 2

D=√8+√152 +√8−√152 

⇒D2=8+√152 +8−√152 +2.√(8+√15)(8−√15)2.2 

=8+2.√64−154 

=8+2.72 =8+7=15

⇒D=√15 Hoặc D=−√15

Mà D>0 nên D=√15