find the value of A and B?

Question

if
A^2+C^2 = 25f
B^2 + C^2 =9f
(A+B-C)^2 + B^2 = 16f

Answer 1

This system of eqns may not be completely specified.

A²+C² = 25f
B² + C² =9f
(A+B-C)² + B² = 16f

Adding 2AC to first eqn
A²+C² = 25f + 2AC

Subtracting second eqn from first eqn:
A²-B² = 25f-9f =16f
Adding this to third eqn:
A² + (A+B-C)² = 32f

Expanding the third eqn:
A²+B²+C² +2AB -2AC-2BC + B² = 16f
(A²+2AB+B²) + B² -2AC-2BC + C² = 16f

In order to add the missing information (the signs of A,B,C), you will have to consider all 8 separate hypotheses:
A +ve/-ve , B +ve/-ve, C +ve/-ve
Try starting with the easy and obvious one: all +ve

Sorry I can't finish it.