Question

Tính x³ - y³ biết x-y=7 và x²+y² = 65

Answer 1

Có : \(x-y=7\Rightarrow x^2-2xy+y^2=49\)

\(\Rightarrow2xy=16\Rightarrow xy=16\)

Lại có :

\(x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)=7.\left(65+16\right)=7.81=567\)

Answer 2

Có :\(x^3-y^3\)=\(\left(x-y\right)\)\(\left(x^2+xy+y^2\right)\)(1)

Có \(x-y=7\)

=> \(\left(x-y\right)^2\)=\(7^2\)

\(x^2-2xy+y^2\)= \(49\)

=>\(65-2xy\)=\(49\)

\(2xy\)\(=\)\(65-49\)

\(2xy=\)\(16\)

\(xy=16:2\)

\(xy=8\)

\(Thay\)\(vào\)\(\left(1\right)\)\(ta\)\(có\)

\(x^3-y^3\)=\(7.\left(65+8\right)\)

\(x^3-y^3=7.73\)

\(x^3-y^3=511\)