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Rufina [12.5K]
3 years ago
10

Prove that if n is a perfect square, then n+1 can never be a perfect square

Mathematics
1 answer:
natka813 [3]3 years ago
8 0

Answer:

Proved

Step-by-step explanation:

To prove that if n is a perfect square, then n+1 can never be a perfect square

Let n be a perfect square

n=x^2

Let n+1 = y^2

Subtract to get

1 = y^2-x^2 =(y+x)(y-x)

Solution is y+x=y-x=1

This gives x=0

So only 0 and 1 are consecutive integers which are perfect squares

No other integer satisfies y+x=y-x=1

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