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The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, find the numbers. |
Answer» Let the two numbers be x and y, y being the bigger number. From the given information, x2 + y2 = 208 ..... (i) y2 = 18x ..... (ii) From (i), we get y2 = 208 − x2. Putting this in (ii), we get, 208 − x2 = 18x ⇒ x2 + 18x − 208 = 0 ⇒ x2 + 26x – 8x − 208 = 0 ⇒ x(x + 26) − 8(x + 26) = 0 ⇒ (x − 8)(x + 26) = 0 ⇒ x can't be a negative number, hence x = 8 ⇒ Putting x = 8 in (ii), we get y2 = 18 x 8 = 144 ⇒ y = 12, since y is a positive integer Hence, the two numbers are 8 and 12. |
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