Question

Stiind ca a-b=1 calculati a×a+b×b-2ab+2a-2b+1 sunt clasa a7-a

Answer 1

$a\cdot a+b\cdot b-2ab+2a-2b+1=a^2+b^2+1-2ab+2a-2b=\\ =(a-b+1)^2= (1+1)^2=\boxed{4}$

Answer 2

$\it a-b=1\ \ \ \ (*) \\ \\ a\cdot a+b\cdot b-2ab+2a-2b+1= a^2-2ab+b^2+2(a-b) +1 = \\ \\ = (a-b)^2 +2(a-b) +1 = (a-b+1)^2 \stackrel{(*)}{=} (1+1)^2 =2^2=4$