Solve the following ? Please

Question

$|x^2-4x+3|=x+1$

1258 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-17T06:12:39

$x=(5+-sqrt17)/2$

If $|x^2-4x+3|=x+1$ , we have $x>=-1$ as $|x^2-4x+3|>=0$ . This gives us the domain of $x$ .

Now we have two possibilities

$x^2-4x+3=x+1$ or $x^2-5x+2=0$ i.e.

$x=(5+-sqrt(5^2-8))/2=(5+-sqrt17)/2$

Observe that both are in domain.

If $x^2-4x+3=-x-1$ or $x^2-3x+4=0$ . But here discriminant is negative $3^2-4×1×4=-7$ . Hence we do not have any solution.