Question

Cho a+b=6, a^2+b^2 = 2010 Tính giá trị biểu thức M=a^3+b^3

Answer 1

\(a+b=6\)

<=>   \(\left(a+b\right)^2=36\)

<=>   \(a^2+2ab+b^2=36\)

<=>   \(2ab=36-a^2-b^2=-1974\)

<=>   \(ab=--987\)

\(a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)=6^3-3.\left(-987\right).6=17982\)

Answer 2

\(a^3+b^3=\left(a+b\right)\left(a^2+2ab+b^2\right)\)

\(=6\left(2010+2ab\right)\)

\(12060+6\left[\left(a+b\right)^2-a^2-b^2\right]\)

\(12060+6\left(36-2010\right)\)

\(=12060-11844\)

\(=216\)

Answer 3

sửa lại 

\(2ab=\left(a+b\right)^2-a^2-b^2\)

\(2ab=36-2010\)

\(2ab=-1974\)

\(\left(a+b\right)\left(a^2-ab+b^2\right)\)

\(6\left(2010-ab\right)\)

\(12060-\left(-5922\right)\)

\(=17892\)