The sum of a number and its reciprocal is 10/3. What is the number?

Question

please help me solve it and check.
thank you very much

And they're asking me to use five step method!

Answer 1

x + 1/x = 10/3
x^2 + 1 = 10x/3
3x^2 - 10x + 3 = 0
(3x - 1)*(x - 3) = 0

x = 1/3, 3

Answer 2

Let x = the number

The reciprocal of x is 1/x, so

x + 1/x = 10/3
Multiply both sides by x
x(x) + x(1/x) = (x)10/3
x^2 + 1 = 10x/3
Multiply both sides by 3
3x^2 + 3 = 10x
3x^2 - 10x + 3 = 0
(3x - 1)(x - 3) = 0
x = 3 and 1/3

The 2 answers are x = 3 and x = 1/3

Answer 3

x + 1/x = 10/3
=>

(x^2 + 1)/x = 10/3
=>

x = 3

Answer 4

Reciprocal is 1 divided by a number.

So,
x + (1/x) = 10/3

Common denominator: 3x
(x)*(3x/3x) + (1/x)*(3/3) = (10/3)*(x/x)
(3x^2)/(3x) + 3/(3x) = 10x/3x

Multiply equation by 3x
3x^2 + 3 = 10x

Subtract 10 from each side
3x^2 - 10x + 3 = 0

Factor
(3x - 1)(x - 3) = 0
3x - 1 = 0, x - 3 = 0
x = 1/3
x = 3

So 1/3 or 3 will work.

Check answers:
1/3:
(1/3) + 1/(1/3) = 1/3 + 3 = 1/3 + 9/3 = 10/3

3:
(3) + (1/3) = 9/3 + 1/3 = 10/3

Answer 5

Let number be x
x + (1 / x) = 10 / 3
3x² + 3 = 10x
3x² - 10x + 3 = 0
(3x - 1) (x - 3) = 0
x = 1 / 3 , x = 3

Answer 6

x + 1/x = 10/3
x^2 + 1 = 10x/3
3x^2 - 10x + 3 = 0
(3x - 1)*(x - 3) = 0

x = 1/3 or x = 3

Answer 7

Let the no.=x
so x+1/x=10/3
or (x^2+1)/x=10/3
Or3(x^2+1)=10x
Or 3x^2+3-10x=0
or 3x^2-10x+3=0
or3x^2-x-9x+3=0
or x(3x-1)-3(3x-1)=0
or (x-3)(3x-1)=0
so x=3 or 3x-1=0
or x=3 or x=1/3
The no.can be 3 or 1/3 ans

Answer 8

The sum of a number and its reciprocal is 10/3.

. . . . . . . . . . . . . n . . . . + . . . . . 1/n . . . . = 10/3

n + 1/n = 10/3

3n^2 + 3 = 10n {multiply by 3n}

3n^2 - 10n + 3 = 0

(3n - 1)(n - 3) = 0

n = 1/3, 3

If you are looking for an integer, 3 is the number

3 + 1/3 = 10/3

9/3 + 1/3 = 10/3

10/3 = 10/3

Answer 9

x+ (1/x)=10/3

(x^2+1)/x=10/3

3x^2+3=10x

3x^2-10x+3=0

(3x-1)(x-3)=0

x=3 or 1/3

Answer 10

n + 1/n = 10/3 10/3 = 3 + 1/3 n + 1/n = 3 + 1/3 n = 3 3 + 1/3 = 3 1/3