Question

Cho a-b=6 và a.b=9.Tính A=a^3-b^3-84

Answer 1

a³-b³-84

=(a-b)² ( a²+ab+b²)-84

6.(a²-2ab+b²+3ab)-84

6[(a-b)²+3ab] -84

6( 6²+3.9)-84

=294

Answer 2

ta có : a\(^3\)- b\(^3\)- 84 = (a-b)(a\(^2\)+ ab +b\(^2\)) - 84

                      = 6*(9+ a\(^2\)+b\(^2\)) -84

ta lại có: (a -b)=6 <=> ( a-b)\(^2\)= 36

<=> a\(^2\)-2ab +b\(^2\)=36 <=>a\(^2\)+b\(^2\)- 18 =36 <=> a\(^2\)+ b\(^2\)= 36 +18 =54

vậy a\(^3\)- b\(^3\)- 84 =6*(9+54)-84 =294