Question

[Thùy Linh]

cho x+y = 6.912 và x² +y² = 33,76244. tính x³ - y³

giúp mik với

Answer 1

[Lê Anh Duy]

x + y = 6,912

\(\Rightarrow\left(x+y\right)^2=47,775744\Rightarrow\left(x^2+y^2\right)+2xy=47,775744\)

\(\Rightarrow33,76244+2xy=47,775744\Rightarrow2xy=14,013304\)

\(\Rightarrow xy=\frac{14,013304}{2}=7,006652\)

Và \(\left(x-y\right)^2=\left(x^2+y^2\right)-2xy=33,76244-14,013304=19,749136\)
\(\Rightarrow x-y=\sqrt{19,749136}=4,444\)

Ta có

\(x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)\) = \(4,444\cdot\left(33,76244+7,006652\right)=181,1778448\)

Answer 2

[Nguyễn Việt Lâm]

Có \(\left\{{}\begin{matrix}x+y=a\\x^2+y^2=b\end{matrix}\right.\)

\(2xy=\left(x+y\right)^2-\left(x^2+y^2\right)\Rightarrow xy=\frac{a^2-b}{2}\)

\(\left(x-y\right)^2=2\left(x^2+y^2\right)-\left(x+y\right)^2\)

\(\Rightarrow x-y=\sqrt{2\left(x^2+y^2\right)-\left(x+y\right)^2}=\sqrt{2b^2-a^2}\)

Vậy:

\(x^3-y^3=\left(x-y\right)^3+3xy\left(x-y\right)=\left(\sqrt{2b^2-a^2}\right)^3+\frac{3\left(a^2-b\right)\sqrt{2b^2-a^2}}{2}\)

Thay \(\left\{{}\begin{matrix}a=6,912\\b=33,76244\end{matrix}\right.\) vào và bấm