Question

Prove that if x is odd, then x² is also odd.

Answer 1

x is an odd number, x = 2k + 1 

{definition of odd} 

x = 2k + 1 

squaring on both sides

(x)² = (2k + 1)² 

x² = 4k² 

4k + 1 = 2(2k² + 2k) + 1 = 2l + 1

x² = 2l + 1 {l = 2k² + 2k} 

∴ x² is an odd number.