Basic math help

[Ande Yashwanth]

View attachment 6594

 

[I like Serena]

Hi Ande Yashwanth! Welcome to MHB! (Smile)

First step would be to multiply out the left hand side.
Did you already do that?
Anyway, being smart about it, we can write the left hand side as:
$$(a+b+c)(b+c-a)=((b+c)+a)((b+c)-a)=(b+c)^2-a^2$$
So we get:
$$(b+c)^2-a^2=\lambda bc$$

Now we want to get rid of the $a^2$.
We can do so by applying the law of cosines:
$$a^2=b^2+c^2 - 2bc\cos\alpha$$
What would we get if we fill that in and simplify further? (Wondering)