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

Răspuns :

[tex]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}[/tex]

[tex]\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[/tex]