The value of (sqrt{5} + 1)^5 - (sqrt{5} - 1)^ | vedclass

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Question

(B) Using the binomial expansion formula $(x+a)^n - (x-a)^n = 2 \left[ {^nC_1} x^{n-1} a + {^nC_3} x^{n-3} a^3 + {^nC_5} x^{n-5} a^5 + \dots \right]$.

Vedclass · Accepted Answer

$352$

Vedclass · Answer

(B) Using the binomial expansion formula $(x+a)^n - (x-a)^n = 2 \left[ {^nC_1} x^{n-1} a + {^nC_3} x^{n-3} a^3 + {^nC_5} x^{n-5} a^5 + \dots ight]$.Here,$x = \sqrt{5}$,$a = 1$,and $n = 5$.Substituting these values:$(\sqrt{5} + 1)^5 - (\sqrt{5} - 1)^5 = 2 \left[ {^5C_1} (\sqrt{5})^4 (1)^1 + {^5C_3} (\sqrt{5})^2 (1)^3 + {^5C_5} (\sqrt{5})^0 (1)^5 ight]$$= 2 \left[ 5 	imes 25 	imes 1 + 10 	imes 5 	imes 1 + 1 	imes 1 	imes 1 ight]$$= 2 \left[ 125 + 50 + 1 ight]$$= 2 	imes 176$$= 352$.

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

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