If ##a^2 + b^2 = 4## and ##(a-b)^2 =2##, what is the value of ##ab##?

1

Given :
##a^2 + b^2 =4##…….1
##(a-b)^2=2##…..2
First expand the 2 equation :
##(a-b)^2=2##
##a^2-2ab+b^2=2##
##a^2+b^2-2ab=2##……..3
put 1 equation into 3 equation :
##a^2+b^2-2ab=2##
##4-2ab=2##
##4-2=2ab##
##2ab=2##
##ab=2/2=1##

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