Question

If x²-5x +1 =0, what is the value of -

`(x + (1)/(x) )`
​

Answer 1

5

Explanation:

Since this equation is not factorable, you can either use the quadratic formula, graph and look for its zeros, or other methods to get it's zeros.

But using the quadratic formula which always spits out a x value gives me:

4.791 and 0.209.

Now let's test both of these values since we have two x values.

`(4.791+(1)/(4.791))` ≈5 (4.9999)

and

`(0.209+(1)/(0.209))` ≈5 (4.9936)

Answer 2

Answer: 5

=================================================

Work Shown:

x^2 - 5x + 1 = 0

x^2 + 1 - 5x = 0

x^2 + 1 = 5x

(x^2 + 1)/x = 5 .... where x is nonzero

(x^2)/x + (1/x) = 5

x + (1/x) = 5

---------------

An alternative method involves solving the original equation using the quadratic formula. After you get the two roots x = p and x = q, you should be able to find that p + 1/p = 5 and also q + 1/q = 5 as well.

In this case,

p = (5 + sqrt(21))/2

q = (5 - sqrt(21))/2