Question

prove that if x is odd then x square is also odd

Answer 1

proof,let x be odd
x=2k+1(for some integer k)
x square =2 (k+1)square
x square =4k square +4k+1
since (4k square +4k)is even (4k square +4k+1)is odd
so,it is true


hope its help you

Answer 2

Prove that if x is odd then x square is also odd

We will suppose x to be odd

Therefore,

x=2k+1 (for some integer k)

$x^{2}$ = $(2k+1)^{2}$

Using the formula

• $(a+b)^{2} =x^{2} +2ab +b^{2}$

$x^{2}$ = 4$k^{2}$ +4k+1

Since ( 4$k^{2}$ +4k)is even (4$k^{2}$ +4k+1)is odd

Therefore It is proved