Question

How do you solve `9u ^ { 2} - 24u + 16=0`?

Answer 1

`u = 4/3" "` with multiplicity `2`

Explanation:

Note that:

`(A-B)^2 = A^2-2AB+B^2`

In our example, both `9u^2 = (3u)^2` and `16 = 4^2` are perfect squares and we find that putting `A=3u` and `B=4`, the middle term matches `-2AB` ...

`0 = 9u^2-24u+16`

`color(white)(0) = (3u)^2-2(3u)(4)+4^2`

`color(white)(0) = (3u-4)^2`

Hence:

`u = 4/3" "` with multiplicity `2`