PROVE THAT NO NUMBER OF THE TYPE 4K+2 CAN BE A PERFECT SQUARE
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Answered by
81
Lemma:
If p is a prime factor of a perfect square, p^2 must also
be a factor of that perfect square.
'
4k+2 = 2(2k+1)
'
2 is a factor of 4k+2 but 2k+1 is odd and cannot have factor 2, so 4k+2 is not divisible by 4, and therefore cannot be a perfect square.
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Answered by
10
Since:
4k+2 = 100
4k =100 - 2
K= 24.5
4k + 2 = 1
4 k = 1-2
4k = -1
k = -1/4
K = -0.25
Hence , no number of type 4k+2can be a perfect sq.
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