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Find The Greatest Integer Less Than Or Equal To (root 3+1)^8 a) 4251 b) 4215 c) 4521 d) 4125

Find The Greatest Integer Less Than Or Equal To (root 3+1)^8


a) 4251


b)  4215


c) 4521


d) 4125

Grade:9

1 Answers

Pratik Tibrewal
askIITians Faculty 37 Points
7 years ago
(root3+1)^8 = 8C0root3^8+ 8C1 root3^7 + 8C2 root3^6 + 8C3 root3^5 + 8C4 root3^4 + 8C5 root3^3 + 8C6 root3 ^2 + 8C7 root3 ^1 + 8C8
(root3-1)^8 = 8C0root3^8 - 8C1 root3^7 + 8C2 root3^6 - 8C3 root3^5 + 8C4 root3^4 - 8C5 root3^3 + 8C6 root3 ^2 - 8C7 root3 ^1 + 8C8
Add both the above equations:
(root3 + 1)^8 + (root3 - 1)^8 = 2*(8C0root3^8+ 8C2 root3^6+ 8C4 root3^4+ 8C6 root3 ^2+ 8C8)
= 2* ( 81 + 28*27 + 70*9 + 28*3 + 1)
= 2* (81 + 756 + 630 + 84 +1 )
= 2* ( 1552)
= 3204
So greatest integer less than or equal to is 3201

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Thanks and Regards,
Pratik Tibrewal
askiitians faculty
BTech


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