Prove that the difference between the squares of two consecutive natural number is equal to their sum
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Let the two consecutive natural numbers be
(x+1) and x
Their square difference = (x+1)²-x²
=x²+1²+2(x)(1) - x²
=1+2x
=2x+1
The sum of numbers = (x+1)+x
=2x+1
Both are equal.
Hence proved.
Example:-
2 and 3
Square difference=3²-2²
= 9-4
= 5
Their sum = 2+3
=5
Both are equal.
(x+1) and x
Their square difference = (x+1)²-x²
=x²+1²+2(x)(1) - x²
=1+2x
=2x+1
The sum of numbers = (x+1)+x
=2x+1
Both are equal.
Hence proved.
Example:-
2 and 3
Square difference=3²-2²
= 9-4
= 5
Their sum = 2+3
=5
Both are equal.
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