The value of (5+1)^ 5 -(5-1)^ 5 is: - Vidyadip

MCQ

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

A
$252$
✓
$352$
C
$452$
D
$532$

✓

Answer

Correct option: B.

$352$

Given, $(\sqrt{5}+1)^{5}-(\sqrt{5}-1)^{5} $
$=(\sqrt{5}+1)^{5}-(\sqrt{5}-1)^{5} $
The even terms will get eliminated.
Hence, we get
$2\left[{ }^5 \mathrm{C}_0+{ }^5 \mathrm{C}_2 5+{ }^5 \mathrm{C}_4 5^2\right]$
$= 2 [1 + 50 + 125]$
$= 2 [176]$
$= 352.$

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