Question

How do you solve `x^2-1=0`?

Answer 1

`color(blue)(x=-1)` or `color(blue)(x=+1)`

Explanation:

Remember "the difference of squares"
`color(white)("XXX")a^2-b^2=(a+b)(a-b)`

Therefore
`color(white)("XXX")x^2-1=0`

`color(white)("XXX")rArr (x+1)(x-1)=0`

`rArr "Either "`
`color(white)("xxxxxxxx"){: ((x+1)=0," or ",(x-1)=0), (rarr x=-1,,rarr x=+1) :}`

Answer 2

`x=1` or `x= -1`

Explanation:

`x^2-1=0`

`:.x^2=1`

`:.x=sqrt1`

`:.x=1` or`x=-1`