2

(√5,3)

The process is as follows

First, the sum of the two sides is greater than the third side.

The difference between the two sides is smaller than the third side.

The approximate value range of c is (1, 3).

Application of Cosine Theorem

Because the obtuse triangle ABC

Therefore, the angle C subtended by C must be greater than 90.

So cosc is negative.

Cosine theorem C = 5-4 COSC

cosc=(-c^2

+5)/4

So (5-c 2) < 0

The solution is c 2 > 5.

-√5