Question

The sum of a whole number and its reciprocal is 10/3 .What is the number.How can you solve this problem.

Answer 1

Answer:

3 is the number.

Step-by-step explanation:

Let the number be x

Sum of the number and it's reciprocal is equal to 10/3

So, we can write,

x+(1/x)=10/3

(x²+1)/x=10/3

Cross multiply.

3(x²+1)=10x

3x²+3=10x

3x²-10x+3=0

We will get a quadratic equation. Now, we proceed to use the factorization method for finding the roots.

3x²-10x+3=0

3x²-9x-1x+3=0

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

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

Now we can find the roots.

3x-1=0

3x=1

x=1/3

x-3=0

x=3

So, x=3,(1/3)

Since x is a whole number (1/3) is not possible.

So the only possible value of x is 3

Thank you.