X²-7x-2=0 x₁=α x₂=β ⇒ a+b=7 ab=-2.
a) (a-b)²+4ab=a²-2ab+b²+4ab=a²+2ab+b²+(a+b)²=7²=49.
b) (a-b)²+3ab=a²-2ab+b²+3ab=a²-2ab+b²+4ab-ab=a²+2ab+b²-ab=(a+b)²-ab=
=7²-(-2)=49+2=51.
c) 2(a-b)²-10=2a²-4ab+2b²+8ab-8ab-10=2a²+4ab+2b²-8ab-10=
2(a+b)²-8ab-10=2*7²-8*(-2)-10=98+16-10=104.
d) (a-b)²/3-ab=((a-b)²-3ab)/3=(a²-2ab+b²-3ab)/3=(a²-5ab+b²)/3=
=(a²-5ab+b²+7ab-7ab)/3=(a²+2ab+b²-7ab)/3=((a+b)²-7ab)/3=
=(7²-7*(-2))/3=(49+14)/3=63/3=21.