Question

The value of $(\sqrt{5}+1{)}^5-(\sqrt{5}-1{)}^5$ is

• A. $252$
• B. $352$
• C. $452$
• D. $532$

Answer 1

The correct option is B $352$

Given, $(\sqrt{5}+1{)}^5-(\sqrt{5}-1{)}^5$
$=(1+\sqrt{5}{)}^5+(1-\sqrt{5}{)}^5$
The even terms will get eliminated.
Hence, we get
$2[{}^5{C}_0+{}^5{C}_{2}5+{}^5{C}_4{5}^2]$
$=2[1+50+125]$
$=2\left[176\right]$
$=352$.