-1

ax+y-2=0 x-ay+3=0 2x+y-a=0

Find a if (a,a) lies inside the triangle formed by these three lines

The Polymath
  • 3
  • This is not true, take $a=i$ and $b=0$. – TheSilverDoe Jan 27 '21 at 20:57
  • @TheSilverDoe There are no inequalities with complex numbers. – Oussema Jan 27 '21 at 21:54
  • Polymath, you should be careful when using AM-GM as it's only true for positive reals. And in this case, it's clear that a and b can be negative. – Oussema Jan 27 '21 at 21:55
  • @Oussema Until you define it. For example, you can define for complex numbers $a \geq b$ iff $a-b$ is a positive real number : it is natural and has sense. – TheSilverDoe Jan 28 '21 at 07:47
  • @TheSilverDoe That's a useless definition. It is clear in the context of an inequality that the variables are reals. – Oussema Jan 28 '21 at 13:51
  • @Oussema Hint : my comment was (maybe) a way to make the OP understand that his/her question needs some clarification....... – TheSilverDoe Jan 28 '21 at 14:46
  • @TheSilverDoe I know. But there are better and more direct ways to go about that. There's nothing stopping you from telling them outright that their question needs further context. I find that the way you did it will only make the poster more confused instead of putting them on the right track. – Oussema Jan 28 '21 at 14:57

1 Answers1

0

Assuming $a,b \in\mathbb{R}$, you have

$$ a^2+2ab+4b^2 = a^2+2ab+b^2+3b^2 = (a+b)^2 +3b^2 \geq 0.$$

Apprentice
  • 69