Thread: There is a problem from sine & cosine chapter

In ∆ABC, AB = (2 – x) cm, BC = (x + 1) cm and angle ABC = 120˚:

a) Show that AC^2 = x^2 – x +7.
b) Find the value of x for which AC has a minimum value.

I’ve done 1st part. But how can I solve 2nd part. Please help me.

Hello, geton!

a) Show that: .

b) Find the value of for which has a minimum value.

You already have: .

Minimize the function: .

We have: .

Therefore: .

Without differentiation, of course



The rest follows.

Originally Posted by Krizalid

Without differentiation, of course



The rest follows.

You mean

But in this way how can I get x = 1/2?

Originally Posted by geton

You mean

But in this way how can I get x = 1/2?

Since , we have
with equality at 2x-1 = 0.
Thus min is achieved at

Thanks.