The sum of two numbers is 37, and the difference of their squares is 185. What is the difference between the two numbers?
The sum of two numbers is 37, and the difference of their squares is 185. What is the difference between the two numbers?
दो संख्याओं का योग 37 है और उनके वर्गों का अंतर 185 है, तो दोनों संख्याओं के बीच का अंतर है:
Detailed Solution & Logic
Correct Answer:
5
Let the two numbers be $a$ and $b$.
Given:
$a + b = 37$
$a^2 - b^2 = 185$
Step 1: Use identity
$a^2 - b^2 = (a - b)(a + b)$
So,
$(a - b)(a + b) = 185$
Step 2: Substitute
$(a - b) \times 37 = 185$
Step 3: Solve
$a - b = \frac{185}{37} = 5$
Final Answer: 5
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