Evaluate the following: (2+ 3)^7+(2- 3)^7 - Vidyadip

Question

Evaluate the following:
$(2+\sqrt3)^7+(2-\sqrt3)^7$

✓

Answer

$(2+\sqrt3)^7+(2-\sqrt3)^7$
$=2\Big[{^7\text{C}}_02^7+{^7\text{C}}_2{2}^5(\sqrt3)^2+{^7\text{C}}_4(2)^4(\sqrt3)^4+{^7\text{C}}_6{2}(\sqrt{3})^6\Big]$
$=2\Big[128+21\times32\times3+35\times8\times9+7\times2\times27\Big]$
$=2\big[128+2016+2520+378\big]$
$=2\big[5042\big]$
$=10084$

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