Question

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

• A. $252$
• B. $352$
• C. $452$
• D. $552$

Answer 1

The correct option is B $352$

Since, ${(\sqrt{5}+1)}^5-{(\sqrt{5}-1)}^5$
$=2\left\{{}^5{C}_1{\left(\sqrt{5}\right)}^4{+}^5{C}_3{\left(\sqrt{5}\right)}^2{+}^5{C}_5.1\right\}$
$=2\{5\times 25+50+1\}$
$=2\left(176\right)=352$