Question
The square of 12 is subtracted from 25 times a whole
number, and the result is equal to the square of that number. Find the square of the difference between the possible values of the whole number.Solution
Let the number be 'x' ATQ, Or, 25x - 122 = x2 Or, x2 - 25x + 144 = 0 Or, x2 - 16x - 9x + 144 = 0 Or, x(x - 16) - 9(x - 16) = 0 Or, (x - 16) (x - 9) =0 So, 'x' = 16 or 9 So, difference between the possible values of the number = 16 - 9 = 7 Therefore, required value = 72 = 49
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