Question

How to solve |x^2 - 5x + 4| = 4? (Why is my solution wrong?)

Answer 1

My solution, that gives off too many roots:
First I split this into two cases:
1) x^2 - 5x + 4 = 4
2) -(x^2 - 5x + 4) = 4; x^2 - 5x + 4 = -4

Solving 1:
x(x - 5) = 0; x = 0 or x = 5.

Solving 2:
x^2 - 5x + 8 = 0;
x = 2 or 3.

The answers in my book say that it's only 0, 5 (so, only the first case is the right one). Why is that?

Answer 2

\(x^2 - 5x + (2.5/2)^2 = -8+ (2.5/2)^2\)

Answer 3

\(x^2 - 5x + (2.5/2)^2 = -8+ (2.5/2)^2\)
\(x^2 - 5x + (6.25/4) = -8+ (6.25/4)\)
\((x-2.5)^2 =(-32+6.25)/4<0\)

See what I am doing?

Answer 4

so, your solutions are clearly imaginary numbers.
(No real solutions.)

Answer 5

Thank you very much! :)

Answer 6

No problem:)