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The difference between two numbers is 5 and the difference between their squares is 65. Find the numbers. |
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Answer» Let the numbers are a and b. Given that difference between both numbers is 5. ∴ a − b= 5. ... (1) Given that difference between their squares is 65. ∴ a2 − b2 = 65. ⇒ (a – b)( a + b) = 65 (∵(a – b)( a + b) = a2 − b2 ) ⇒ 5(a + b) = 65 ⇒ a + b = \(\frac{65}{5}=13.\) … (2) Now, adding equations (1) & (2), we get (a – b) + ( a + b) = 5 + 13 ⇒ 2a = 18 ⇒ a = \(\frac{18}{2}=9.\) Now, putting a = 9 in equation (1), we get 9 – b = 5 ⇒ b = 9 – 5 = 4. Hence, the numbers are 4 and 9. |
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