Question

Find two consecutive numbers such that the difference of their squares is 65

Answer 1

let us take the two consecutive integers as

x and x+ 1

squaring : as given in the question

( x+1)2 - x2 = 65

( x2+ 1 + 2x) - x2 = 65

x2 + 1 + 2x - x2 = 65

2x = 64

x = 32

therefore the consecutive numbers are

32 and 33

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