gr8 jake bhaiya
1. If x = 2 + 5i (where i2 = - 1) and 2(1/1!9! + 1/3!7!) + 1/5!5! = 2a/b!, then the value of (x3 - 5x2 + 33x - 19) is equal to
(A) a
(B) b
(C) a - b
(D) a + b
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4 Answers
Zuko Alone
·2010-04-08 11:02:56
2\left(\frac{1}{1!.9!}+\frac{1}{3!.7!} \right)+\frac{1}{5!5!} \\\\=\frac{1}{10!}\left( \begin{pmatrix} 10\\1 \end{pmatrix}+\begin{pmatrix} 10\\3 \end{pmatrix}+\begin{pmatrix} 10\\5 \end{pmatrix}+\begin{pmatrix} 10\\7 \end{pmatrix}+\begin{pmatrix} 10\\9 \end{pmatrix}\right) \\\\=\frac{512}{10!}
Now,
x^3-5x^2+33x-19 \\=(x-2)^3+(x-2)^2+25(x-2)+35 \\=-125i-25+125i+35 \\=10
B is the answer.
Hari Shankar
·2010-04-08 22:46:06
Another method:
http://www.goiit.com/posts/list/algebra-in-complex-numbers-if-x-2-5i-then-the-value-of-x-3-5x-990384.htm#1194717