<p>I really can't figure this problem out. I systematically go through all of the answer options, and set the t equal to x+(1/x), but I can never get it. The question is:</p>
<p>▼x = x + (1/x)
▼x = t
What is one possible value of t?
Options:
a.) 1
b.) 0
c.) -1
d.) -2 (correct answer)
e.) -3
If someone could go through this problem step-by-step, I'd be very grateful.</p>
<p>Wanna take a picture of the question or scan it? I’m confused.</p>
<p>I’ll just type the whole problem out. Here it goes:</p>
<p>Let ▼x be defined as x + (1 / x) for all nonzero integers x. If ▼x = t, where t is an integer, which of the following is a possible value of t?
A.) 1
B.) 0
C.) -1
D.) -2 (correct answer)
E.) -3</p>
<p>Thanks very much.</p>
<p>okay well sorry if my explanation is kinda weird but this is how I got it: </p>
<p>From the information in the question, you set t = x + (1/x) </p>
<p>Then you can plug in the answer choices. If you try 1, you get 2. But 2 is not in the
answer choices so try a different number. 0 doesn’t work because you can’t divide 1/0, and the results for -3 and -2 aren’t in the answer choices either. But if you try -1,
you get -2, which is an answer choice. The second part of the equation is a ▼x right? so there is no definite value for x. Remember, the question is asking for a possible value of
t not x. That’s the trick. </p>
<p>Sorry if I confused you but if my reasoning is wrong, you can just totally ignore this ^^"</p>
<p>thanks. i see it now.</p>
<p>For x a positive integer: t = x + 1/x is an integer when x=1 – i.e. t = 2. That’s the only solution for positive x since for x = 2 or greater t is always an integer plus a small fraction.</p>
<p>For x a negative integer t = x + 1/x is an integer when x = - 1 – i.e. t = -2. That’s the only solution for negative x. For x= -2 or greater t is always a negative integer less a small fraction.</p>
<p>So the two solutions are t = 2 and t = -2. Only t = -2 is offered as a choice.</p>