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

quadratic equation solution7 quadratic equation solution7

- Back to worksheet
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- Relationship Between Coefficients and roots
- Roots of Cubic equation
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- Roots of Polynomial of Degree5