Question

If x^2−14x+1=0, what is the value of
x+1/x?

Answer 1

\(\frac{x+1}{x}\)?

Answer 2

no \[x + \frac{ 1 }{ x }\]

Answer 3

@satellite73

Answer 4

you have to find (x^2 +1)/x

from the given equation, you can easily see what x^2 +1 is

rest is a piece of cake.

Answer 5

huh?

Answer 6

x^2 - 14x + 1 =0
so x^2 +1 = ?

Answer 7

14x?

Answer 8

right

and you have to find the value of (x^2 + 1)/x

Answer 9

x = 14, 13 right?

Answer 10

14,13 ? what ?

Answer 11

oh...i remember now...the sum of the roots and its reciprocal of a quadratic equation is just -b

Answer 12

thus -b = 14

Answer 13

thats not true.
Thats only true when a=c=1, which was your case here.

Answer 14

not 1, its true when a=c.

Answer 15

1) find the zeros, \(x_1\) and \(x_2\)
2) compute \(x_1+\frac{1}{x_1}\)

Answer 16

oh....what if \[a \neq c \]?

Answer 17

if a not equals c, then thats not true
then you might need to find the roots separately , or see if anything alternative is applicable.
In this case, you don;t need to find the respective roots.