Question

How do you solve `y^2-6y+8=0`?

Answer 1

Factor the left side to find
`color(white)("XXX")y=2 or y=4`

Explanation:

Given
`color(white)("XXX")y^2-6y+8=0`

Factoring the left side expression
`color(white)("XXX")(y-4)(y-2)=0`

which implies
either
`color(white)("XXX")(y-4)=0 rarr y=4`
or
`color(white)("XXX")(y-2)=0 rarr y=2`

Answer 2

`{2,4}`

Explanation:

`y^2-6y+8=0`
`(y-2)(y-4)=0`
`(y-2)=0 => y=2`
`(y-4)=0 =>y=4`
`{2,4}`

Answer 3

`y=2` or `y=4`

Explanation:

Method of factoring:

`y^2-6y+8=0`
`(y-2)(y-4)=0`
`y-2=0` or `y-4=0`

Solving for `y`, gives `y=2` or `y=4`

Method of quadratic equation:

`y=(6+-sqrt(36-4(1)(8)))/(2(1))=(6+-sqrt(4))/(2)`
`y=2` or `y=4`

Method of graphing:
graph{x^2-6x+8 [-0.927, 9.073, -1.44, 3.56]}