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Question
The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
Solution
Let the smaller numbers be x
Then according to question,
The larger number be = 2x - 5, then
(2x - 5)2 - x2 = 88
4x2 - 20x + 25 - x2 - 88 = 0
3x2 - 20x - 63 = 0
3x2 - 27x + 7x - 63 = 0
3x(x - 9) + 7(x - 9) = 0
(x - 9)(3x + 7) = 0
x - 9 = 0
x = 9
Or
3x + 7 = 0
3x = -7
x = -7/3
Since, x being a positive integer so, x cannot be negative,
Therefore,
When x = 9 then larger number be
2x - 5 = 2(9) - 5 = 18 - 5 = 13
Thus, two consecutive number be either 9, 13.
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