Quadratic Equation Solution9





In this page quadratic equation solution9 we are going to see solution of the word problems of the topic quadratic equation.

Question 16

A two digit number is such that the product of its digits is 12. When 36 is added to this number the digits are interchanged. Find the numbers.

Solution:

Let "x y" be the required two digit number

A two digit number such that the product of its digits is 12

 x(y) = 12

   y = 12/x  ---- (1)

When 36 is added to the number the digits are interchanged

 x y + 36 = y x

10 x + y + 36 = 10 y + x

10 x - x + y - 10 y = -36

 9 x - 9 y = -36

 Now we are going to divide the whole equation by 9,so we get

 x - y = -4  --- (2)

 Now we are going to apply the value of y that is first equation in the second equation.

            x - (12/x) = -4

         x² - 12  = - 4 x

         x² + 4 x - 12 = 0

         x² + 6 x - 2 x - 12 = 0

   x (x + 6) - 2 (x + 6) = 0

 (x - 2) (x + 6) = 0

 x - 2 = 0             x + 6 = 0

 x = 2                     x = -6

To get the value of y we have to apply 2 instead of x in the first equation

          y = 12/x

          y = 12/2

          y = 6

Therefore the required two digit number is 26

Verification:

 A two digit number such that the product of its digits is 12

 2 (6) = 12

  12 = 12

When 36 is added from the number the digits are interchanged

26 + 36 = 62

      62 = 62

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