Math question and how to check it?

Question

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

I think it is 1/3, but I am not for sure. Need help

Also how would you check your answer to this problem.

Answer 1

let x the number

x+1/x=  10/3

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

3 ( x^2+1)= 10 x

3x^2+3= 10x

3x^2-10x+3= 0

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

3x-1= 0

x= 1/3

x-3= 0

x= 3

there are 2 answers for this , 3 and 1/3

check

x+1/x= 10/3

3 + 1/3= 10/3

(9+1)/3= 10/3

10/3= 10/3

x=1/3

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

10/3= 10/3

Answer 2

You are right...

to check it you..

do 1/3 + 3/1 = 3.33333333333

and if you put 10/3 in your calc you get the same answer...

Answer 3

call the number a.

a + 1/a = 10/3

a^2 + 1 = 10a/3

3a^2 + 3 = 10a

3a^2 - 10a +3 = 0

now solve the quadratic equation in the way that suits you best. I am going to factorise.

3a^2 -a -9a + 3 = 0

a(3a-1) -3(3a-1)

(a-3)(3a-1) = 0

a = 3 or a = 1/3

both are valid answers unsurprising since the recipricol of one is the other.

You would check it by simply checking if the condition is true for your number.

with the answer of 1/3 the recricol of it is 3.

1/3 + 3 = 10/3 so it is ture for 1/3 so this is a valid solution

Answer 4

You are right. Here's the algebra behind it..

x + 1/x = 10/3

Multiply everything by x:

x² + 1 = 10x/3

3x² + 3 = 10x

3x² - 10x + 3 = 0

And that factorises as:

(3x-1)(x-3)

Therefore the two numbers are 3 and 1/3.

Hope this helps!

Answer 5

Well, let's take your proposed answer of 1/3.

So the first number you have is, of course, 1/3.

It's reciprocal is 3/1, which is equal to 9/3.

1/3 + 9/3 = 10/3

Answer 6

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

common denom = 3x

3x^2 + 3 = 10x

3x^2 -10x+ 3 =0

(3x-1)(x -3  ) = 0

so by the zero property there are 2 answers

(3x-1) = 0 or (x -3  ) = 0

3x=1

x = 1/3 or x = +3