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The difference between two positive numbers is 3. If the sum of their squares is 369, then the sum of the numbers is1). 812). 333). 274). 25 |
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Answer» Let the two numbers be a and b Now as per the given INFORMATION, a – b = 3….(1) a2 + b2 = 369…..(2) From (1), a = b + 3 Put the value of a in equation (2) a2 + b2 = (b + 3)2 + b2 = b2 + 9 + 6b + b2 = 369 ⇒ 2b2 + 6b + 9 = 369 ⇒ 2b2 + 6b – 360 = 0 ⇒ b2 + 3b – 180 =0 ⇒ (b - 12) (b + 15) = 0 ⇒ b = 12(b is not equal to 15 because b is positive) Put the value of b in equation (1) ∴ a = 12 + 3 = 15 Thus sum of two numbers = a + b = 15 + 12 = 27. |
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