Question

Prove that any number of the form 4x+2 can never be a perfect square.

Answer 1

4x+2=2(2x+1)

Now 2x+1 is an odd number.
So 4x+2 cannot be a square number because the factor 2 will occur only once whereas in a square number each factor should occur even no. of times.

Answer 2

A number of the form 4x+2 can never be a perfect square.

GIVEN: Several form 4x+2
TO PROVE: A number of the form 4x+2 can never be a perfect square.
SOLUTION:

As we are given in the question,

Several form 4x+2

Therefore,

It can be further modified into,

4x+2=2(2x+1)

where x is a natural number.

Implying that,

x = 1,2,3,4,5,6,7,8,9,........x.

So then,

2x+1  will be an odd number.

And it won't have 2 as a factor.

So,

2(2x+1) will not have all factors which are repeated, which is necessary for 4x+2 to be a perfect square.

Therefore,

A number of the form 4x+2 can never be a perfect square.

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