SOLUTION: If x+1/x=1, find the value of x^2+3x+1/x^2+7x+1

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Question 1036411: If x+1/x=1, find the value of x^2+3x+1/x^2+7x+1
Found 2 solutions by Aldorozos, josgarithmetic:
Answer by Aldorozos(172) About Me  (Show Source):
You can put this solution on YOUR website!
If the first part of the problem refers to (x+1)/x = 1 we can multiply both sides of the equation by x. Then we get x+1 = x. There is not any real number that if one is added to the number to give us the same number. There for there is not any real solution to this equation.
If the first part refers to x + 1/x = 1. Then we will use x as common denominator and we will have (x^2+1)/x = 1. We multiply both sides by x. We get x^2+1 = x Adding -x to both sides we get x^2-x+1 = 0. This is a quadratic equation. However there is not any real number that is a solution to this equation. However, there are two imaginary numbers that are solutions.
There is a possibility that some information is missing in this problem.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
If,... what?

x+1/x=1
x%2B1%2Fx=1
x%5E2%2B1=x
x%5E2-x%2B1=0
x=%281%2B-+sqrt%281-4%2A1%2A1%29%29%2F2
x=%281%2B-+sqrt%28-3%29%29%2F2
x=%281%2B-+i%2Asqrt%283%29%29%2F2-----------not a real couple of values, so maybe not what you have.

(x+1)/x=1
%28x%2B1%29%2Fx=1
x%2B1=x
IMPOSSIBLE.

The imaginary pair of values for x is what you want. Just make the necessary substitution, simplify, and evaluate both results.