Question

the sum of a number and its reciprocal is 10/3 find the number

Answer 1

x+1/x=10/3

By taking LCM

x²+1/x=10/3

By cross multiplication

10x=3x²+3
3x²-10x+3=0

By spliting the middle term

3x²-x-9x+3=0

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

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

x=3 , x= 1/3

Answer 2

The  value of the number  are $3\ and \ \frac{1}{3}$ .

Step-by-step explanation:

Given:

A number and its reciprocal  sum is $\frac{10}{3}$ .

To Find:

The  value of the number.

Solution:

As given: a number and its reciprocal  sum is $\frac{10}{3}$ .

Let number is P.

$P+\frac{1}{P} =\frac{10}{3}$

$\frac{P^{2}+1 }{P} = \frac{10}{3}$

$3P^{2} +3 = 10P$

$3P^{2} -10P +3 =0$

$3P^{2} -9P -P +3 =0$

$3P(P-3) - 1(P-3) =0$

$(3P-1) (P-3) =0$

$P=3\ and \ \frac{1}{3}$

Thus, the  value of the number are  $3\ and \ \frac{1}{3}$.