Question

When 43 is divided by x, the remainder is x-5. If x is a natural number, how many solutions are there for x?​

Answer 1

Given,

43 divided by x gives the remainder x - 5

To find,

Number of solutions of x

Solution,

According to the question, we have the equation

                                $\frac{43}{x} = x - 5\\x(x - 5) = 43\\x^{2} - 5x -43 = 0$

x cannot be zero here or left hand side of the equation will become infinity.

Solving the quadratic equation, we have roots  $\frac{5}{2} + \frac{\sqrt{197} }{2}, \frac{5}{2} - \frac{\sqrt{197} }{2}$.

Clearly both the roots are irrational.

Therefore x has no natural number solution.

     

Answer 2

43 divided by x gives the remainder x-5.

TO Find,

     Number of solution of x.

Solution,

 According to the question,we have the equation

           43/x=x-5

           x(x-5)=43

           x^2-5x-43=0

 x cannot be zero here or left hand side of the equation will become  infinity.

 solving the quadratic equation,we have roots 5/2+^197/2,5/2-^197/2.

 Clearly both the roots are irrational.

Therefore X has no natural number solution.