Question

If x and y are even, then x²+ y² are also even.

Answer 1

ANSWER

We know that any odd positive integer is of the form 2q+1, where q is an integer.

So, let x=2m+1 and y=2n+1, for some integers m and n.

we have x

2

+y

2

x

2

+y

2

=(2m+1)

2

+(2n+1)

2

x

2

+y

2

=4m

2

+1+4m+4n

2

+1+4n=4m

2

+4n

2

+4m+4n+2

x

2

+y

2

=4(m

2

+n

2

)+4(m+n)+2=4{(m

2

+n

2

)+(m+n)}+2

x

2

+y2=4q+2, when q=(m

2

+n

2

)+(m+n)

x

2

+y

2

is even and leaves remainder 2 when divided by 4.

x

2

+y

2

is even but not divisible by 4.

Answer 2

Answer:

so x+y=2m+2n =2(m+n) and since x+y is two times the integer m+n then x+y is even

therefore if x and y are even,then x+y is even

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