Question:
Write the number 51 as the difference of the squares of two consecutive natural numbers and find the numbers . I know the answer but not the steps.
Answer:
Let the two consecutive natural numbers are x and x + 1
Given, the difference of the squares of two consecutive natural numbers = 51
=> (x + 1)2 - x2 = 51
=> x2 + 2x + 1 - x2 = 51
=> 2x + 1 = 51
=> 2x = 51 - 1
=> 2x = 50
=> x = 50/2
=> x = 25
So, the numbers are 25, 25 + 1 = 25, 26
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