11-1=10 11=10+1 multiply and divide r.h.s with 1-1 11= (10+1)(1-1) / (1-1) 11= (9+1+1)(1-1) / (1-1) 11= [9(1-1)+(1+1)(1-1)] / (1-1) ------->(a+b)(a-b)=a²-b² 11=9(1-1)/(1-1) + (1²-1²)/(1-1) 11=9 + (1-1)/(1-1) 11=9+1 do the same above process again, we get 11=8+1 this can be written as 11=9 => 11=10-1 => 10-1=11 add 19 and 5 on both sides in different equations, we get 29-1=30, 15-1=16 hence proved