Topic Content:
- Problems Leading to Quadratic Equations
Example 7.3.1:
The difference of the squares of two positive integers is 325 and their difference is 5. What are the numbers?
Solution:
Let the two numbers be x and y
⇒ x – y = 5 ……….(i)
and
⇒ x2 – y2 = 325 ………….(ii)
⇒ x = y + 5 ………..(iii)
Substitute for x in equation (ii)
(y + 5)2 – y2 = 325
y2 + 10y + 25 – y2 = 325
10y + 25 = 325
10y = 300
y = \( \frac{300}{10} \)
⇒ y = 30
Substitute for y in equation (iii)
x = y + 5 ………..(iii)
x = 30 + 5
⇒ x = 35
Check:
| 352 – 302 = 325 | or | x – y = 5 |
| 1,225 – 900 = 325 | or | 35 – 30 = 5 |
| 325 = 325 | or | 5 – 5 |
Example 7.3.2:
The sum of the squares of two integers is 369 and their difference is 3. What are the numbers?
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