If ABC is a triangle with sides a, b , c and opposite angles alpha, beta and gamma. If alpha=3*beta, prove that (a-b)^2*(a+b)=b*c^2?
So, if #alpha=3*beta# , prove that #(a-b)^2*(a+b)=b*c^2#
Angle #alpha# is opposite of side a, angle #beta# is opposite of b, and #gamma# is opposite of c.
So, if
Angle
1 Answer
Using the Law of Sines, the Law of Cosines, the sine triple angle formula and a little Alpha help factoring, I've proven something close, which Is probably the correct formulation:
Given triangle ABC,
Explanation:
I think I can almost get there.
I'll write the angles A, B, and C to keep to standard notation.
Let's write the Law of Sines:
Let's write the Law of Cosines:
Yikes. I'll ask Alpha to factor.
Nice. It's really a shame Euler or Gauss didn't have a computer.
So if