Using properties of determinats, prove that a2 2ab b2 b2 a2 2ab 2ab b2 a2 = (a3 + b3)2 Share with your friends Share 15 Priyanka Kedia answered this Δ=a22abb2b2a22ab2abb2a2=a2+b2+2ab2abb2a2+b2+2aba22aba2+b2+2abb2a2 C1→C1+C2+C3=a+b22abb2a+b2a22aba+b2b2a2=a+b212abb21a22ab1b2a2 Take common a+b2=a+b202ab-b2b2-a21a22ab0b2-a2a2-2ab R1→R1-R3 and R3→R3-R2 =-a+b2a2-2ab2ab-b2-b2-a22=-a+b22a3b-a2b2-4a2b2+2ab3-b4-a4+2a2b2=a+b2a4+b4+2a3b+2ab3-3a2b2=a+b2a2+b22+2a2+b2ab-a2b2=a+b2a2+b2-ab2=a3+b32Hence proved. 8 View Full Answer
