Question

In base x system, 1/5 and 0.17bar are numerals for same number. Find x

Answer 1

Given:  Base x system , 1/5 and 0.17 bar are numerals for same number.

To find: The value of x?

Solution:

• Now we have given a number as 0.17 bar.

• Let the number be y.

• Then y = 0.17 bar = 1/5

• Now we have given base x system, so:

• Multiplying by x^2, we get:

                   x²y = 17.17 bar

                   y(x^2 - 1 ) = 17

                   y = 17 / (x^2 - 1 )

                   17/(x^2 - 1 ) = 1/5

• Now converting  17 & 5 into decimal, we get:

                   17 = 1(x)  + 7(x^0)  

                   17 = x + 7

• Similarly:

                   5 = 5(x^0) = 5

• Now:

                   ( x  + 7   ) / (x^2 - 1 )  = 1/5

                   5x + 35 = x^2 - 1

                   x^2 - 5x - 36 = 0

                   x^2 - 9x + 4x  - 36 = 0

                   x(x - 9) + 4(x - 9) = 0

                   (x + 4) (x - 9) = 0

                   x  = 9

Answer:

               So the value of x is 9.