Question -
Answer -
Let smaller number = x
Then larger number = 2x тАУ 5
According to the condition,
(2x тАУ 5)2 тАУ x2 = 88
=> 4x2 тАУ 20x + 25 тАУ x2 тАУ 88 = 0
=> 3x2 тАУ 20x тАУ 63 = 0
=> 3x2 тАУ 27x + 7x тАУ 63 = 0
=> 3x (x тАУ 9) + 7 (x тАУ 9) = 0
=> (x тАУ 9) (3x + 7) = 0
Either x тАУ 9 = 0, then x = 9
or 3x + 7 = 0, then x = тИТ73 which is not possible
Smaller number = 9
and greater number = 2x тАУ 5 = 2 x 9 тАУ 5 = 18 тАУ 5 = 13
Hence numbers are 13, 9