Question

Cho a³ + 3ab² = 63 và b³ + 3a²b = 62. Tính giá trị M = a² - b²

Answer 1

Ta có :

\(\left\{{}\begin{matrix}a^3+3ab^2=63\\b^3+3a^2b=62\end{matrix}\right.\Rightarrow a^3+3a^2b+3ab^2+b^3=125\Rightarrow\left(a+b\right)^3=125\Rightarrow a+b=5\)

\(\left\{{}\begin{matrix}a^3+3ab^2=63\\b^3+3a^2b=62\end{matrix}\right.\Rightarrow a^3-3a^2b+3ab^2-b^3=1\Rightarrow\left(a-b\right)^3=1\Rightarrow a-b=1\)

\(\Rightarrow M=a^2-b^2=\left(a+b\right)\left(a-b\right)=5.1=5\)

Vậy \(M=5\)

Học tốt !

Answer 2

\(a^3+3ab^2+b^3+3a^2b=63+62=125=\left(a+b\right)^3\)

\(\Rightarrow a+b=5\)

\(a^3+3ab^2-b^3-3a^2b=63-62=1=\left(a-b\right)^3\)

\(\Rightarrow a-b=1\)

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

Mà \(a+b=5;a-b=1\)

\(\Rightarrow a^2-b^2=5.1=5\)

Vậy ...