Question

the sum of number and reciprocals is 10/3 find the number

Answer 1

Let the number be x,

x + 1/x = 10/3

(x²+1)/x = 10/3

3(x²+1) = 10x

3x² + 3 - 10x = 0

3x² - 10x +3 = 0

3x² - (9 + 1)x + 3 = 0

3x² - 9x -x + 3 = 0

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

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


x = 3 or x = 1/3



Now, required number is 3 or 1/3


I hope this will help you


(-:

Answer 2

Hiii friend,



Let the number be X.

Reciprocal of X in 1/X.


According to question,


Sum of Number and reciprocal = 10/3


X + 1/X = 10/3


X²+1 = 10X/3


3(X²+1) = 10X


3X²+3 = 10X


3X²-10X+3 = 0


3X²-9X - X + 3 = 0


3X(X-3) -1(X-3) = 0


(X-3) (3X-1) = 0


(X-3) = 0 OR (3X-1) = 0


X = 3 OR X = 1/3

Hence,


Required Number = X = 3



HOPE IT WILL HELP YOU.... :-)