Evaluate the following: ( 3+1)^5-( 3-1)^5 - Vidyadip

Question

Evaluate the following:

$(\sqrt3+1)^5-(\sqrt3-1)^5$

✓

Answer

$(\sqrt3+1)^5-(\sqrt3-1)^5$

$=2\big[{^5\text{C}}_1(\sqrt3)^4+{^5\text{C}}_3(\sqrt3)^2+{^5\text{C}}_5\big]$

$=2\big[5\times9+10\times3+1\big]$

$=2\big[45+30+1\big]$

$=2\big[76\big]$

$=152$

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