Question

x is an integer. x not equal to 1. explain why (x squared minus 1) - (x - 1)squared is always an even integer

Answer 1

`\sf\\Here,\\x \in Z,\ x\\e 1.\\Now,\\(x^2-1)-(x-1)\\=(x-1)(x+1)-(x-1)\\=(x-1)(x+1-1)\\=x(x-1)\\`

`\sf\\\textsf{Let x be an odd integer. Then, (x - 1) will be an even integer. }\\\textsf{The product of odd integer and even integer is always an even integer.}\\\textsf{Hence, }x(x-1) \textsf{ will be an even integer in this case.}`

`\sf\\\textsf{Let x be an even integer. Then, }(x-1)\textsf{ will be an odd integer.}\\\textsf{In this case also, }x(x-1) \textsf{ will be even integer because the product of even and}\\\textsf{odd integer is an even integer again.}`