Question

1 1 1 Prove that a b C = (b-c)(c - a)(a - b)(a +b+c). 3 a 3 63 C3 C​

Answer 1

Answer:

Step-by-step explanation:

L.H.S.=∣∣∣∣b+c c+a a+b a−b b−c c−a

Applying C2→C2−C3

=∣∣∣∣b+cc+aa+b−b−c−aabc∣∣∣∣

Applying C1→C+C2

=∣∣∣∣cab−b−c−aabc∣∣∣∣  

=−1∣∣∣∣cabbcaabc∣∣∣∣

=−1[c3−abc−bac+b3+a3−abc]

=3abc−a3−b3−c3=R.H.S.