Question

Solve the following equation:

$\sqrt{x^2+2x+1}-\sqrt{x^2-4x+4}=3$

Answer 1

$\sqrt{x^2+2x+1}-\sqrt{x^2-4x+4}=3$

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

When $x\in [2,\infty ),x+1-x+2=3$ which is always true

When $x\in [-1,2],x+1+x-2=3⟹x=2$

When $x\in (-\infty ,-1],-x-1+x-2=3$ i.e $-3=3$ which is not possible

So the solution is any value in this interval $[2,\infty )$