Let $\lbrack x\rbrack$ donate the greatest integer less than or equal to $x.$ If $x = (\sqrt{3} + {1)}^{5}$, then $\lbrack x\rbrack$ is equal to

Question

Dr. Abubacker · Accepted Answer

(d)
Now, $\left( \sqrt{3} + 1 ight)^{5} = \left( \sqrt{3} ight)^{5} + \ ^{5}C_{1}\left( \sqrt{3} ight)^{4} + \ ^{5}C_{2}\left( \sqrt{3} ight)^{3}$
+$\ ^{5}C_{3}\left( \sqrt{3} ight)^{2} + \ ^{5}C_{4}\left( \sqrt{3} ight) + \ ^{5}C_{5}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  = 9\sqrt{3} + 45 + 30\sqrt{3} + 30 + 5\sqrt{3} + 1$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  = 76 + 44\sqrt{3}$
$	herefore\left\lbrack \left( \sqrt{3} + 1 ight)^{5} ightbrack = \left\lbrack 76 + 44\sqrt{3} ightbrack$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  = \lbrack 76brack + \lbrack 44 	imes 1.732brack$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  = 76 + 76 = 152$

Q. Let $\lbrack x\rbrack$ donate the greatest integer less than or equal to $x.$ If $x = (\sqrt{3} + {1)}^{5}$, then $\lbrack x\rbrack$ is equal to

Explanation

Reviewed by Dr. Abubacker

Want more practice?