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
PRAKHAR GUPTA , 11 Years ago
Grade 9
Algebra> greatest-integer...
1 Answers
Pratik Tibrewal
Last Activity: 11 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
Thereis something wrong in your options
Thanks and Regards,
Pratik Tibrewal
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