If +3 3 +5 5 =0 , +3 3 +5 5 =0 and 3 +27 9 +125 15 = ( ^2-4 ) ( +3 +5 ) , then is equal to

Step-by-step solution

Given, +3 3 +5 5 =0 ...(i) +3 3 +5 5 =0 ...(ii) 3 +27 9 +125 15 = ( ^2-4 ) ( +3 +5 ) ...(iii) To find, = ? Let a= +i aligned & b=3( 3 +i 3 ) & c=5( 5 +i 5 ) aligned Consider, a+b+c aligned =( +i )+ & 3( 3 +i 3 ) & +5( 5 +i 5 ) aligned aligned =( +3 & 3 +5 5 ) & +i( +3 3 +5 5 ) aligned =0 a^3+b^3+c^3=3 a b c , if a+b+c=0 aligned ( +i )^3+ 3( 3 + & i 3 ) ^3 & + 5( 5 +i 5 ) ^3 aligned array r =3( +i ) 3( 3 +i 3 ) 5( 5 +i 5 ) array aligned =[ 3 +i 3 )+ & 27( 9 +i 9 ) & + 25( 15 +i 15 ) aligned array r =45( +i )( 3 +i 3