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Question
The sum of the square of two numbers is 233. If one of the numbers is 3 less than twice the other number. Find the numbers.
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Solution
Let the numbers be x, 2x - 3. Then,
x2 + (2x-3)2 = 233
⇒ x2 + 4x2 + 9 - 12x = 233
⇒ 5 x2 -12x - 224 = 0
⇒ 5 x2 - 40x + 28x - 224 = 0
⇒ 5x (x - 8) + 28(x - 8) = 0
⇒ (5x + 28)(x - 8) = 0
⇒ x = 8 (As the number have to be natural number)
⇒ Other number = 2 x 8 - 3 =13
Hence, the numbers are 8 and 13
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