if x+1/x=3 how much is x^2+1/x^2?

Answer 1

7
x+1/x=3 => (x+1/x)^2 = 9
but (x+1/x)^2 = x^2 + 1/x^2 + 2 = 9
hence x^2 + 1/x^2 = 7
EDIT: i see that me and sweet and simple understood your question differently.
If you mean (x+1)/x = 3, see her solution
If you mean x + (1/x) = 3, see my solution.
EDIT: thank you sweet and simple

Answer 2

3

Answer 3

(x+1)/x = x/x + 1/x = 1 + 1/x

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

Since 1+ 1/x = 3, that means that 1/x = 2

So
1 + 1/x*1/x = 1 + 2*2 = 5

Answer 4

Depends on exactly what you mean.

Without parentheses, your problem means:

x + (1/x) = 3

But others are assuming you mean:

(x+1)/x = 3

In the former case,

x + (1/x) = 3
x^2 + 1 = 3x
x^2 - 3x + 1 = 0
x = (3 +/- sqrt(5)) /2

In the latter case:

(x+1)/x = 3
x + 1 = 3x
x = 1/2

Assuming the latter,

(x^2 + 1)/(x^2) =
(1/4 + 1)/1/4 =
(5/4) / (1/4) =
5

Answer 5

x+1/x=3

(x+1/x)^2 = 3^2

x^2 + 2 + (1/x)^2 = 9

x^2 + 1/x^2 = 7

Answer 6

x+1/x=3
x+1 =3x
2x=1
x =1/2

so x^2+1/x^2
= [(1/2)^2 +1] / (1/2)^2
=[1/4 +1] /1/4
=5/4 *4
=5

Edit: Hey starwhitedwarf....u r so sweeet!!!