Quadratic Equation Solution7





In this page quadratic equation solution7 we are going to see solution of the word problems of the topic quadratic equation.

Question 13

Two positive numbers differ by 4 and their product is 192. Find the numbers.

Solution:

Let "x" and "y" are two positive numbers

it differs by 4

x - y = 4

 x = 4 + y   --- (1)

their product is 192

 x y = 192

   y = 192/x --- (2)

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

              x = 4 + (192/x)

              x = (4 x + 192)/x

             x² = 4 x + 192

           x² - 4 x - 192 = 0

          x² - 16 x  + 12 x - 192 = 0

      x (x - 16) + 12 (x - 16) = 0

    (x - 16) (x + 12) = 0

        x - 16 = 0          x + 12 = 0

         x = 16                x = -12

To find another number that is y we have to apply this value in the second equation

y = 192/x

 y = 192/16

 y = 12

Since it is positive number we have to choose 16 for x.

Verification:

it differs by 4

16 - 12 = 4

  4 = 4

their product is 192

(16) (12) = 192

 192 = 192

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