a) Vì x + y = 2
\(\Rightarrow\left(x+y\right)^2=4\)
\(\Rightarrow x^2+y^2+2xy=4\)
\(\Rightarrow10+2xy=4\)
\(\Rightarrow2\left(5+xy\right)=4\)
\(\Rightarrow5+xy=2\)
\(\Rightarrow xy=-3\)
Do đó:
\(x^3+y^3=\left(x+y\right)\left(x^2+y^2-xy\right)\)
\(\Rightarrow x^3+y^3=2\left[10-\left(-3\right)\right]\)
\(\Rightarrow x^3+y^3=2\left(10+3\right)\)
\(\Rightarrow x^3+y^3=2.13\)
\(\Rightarrow x^3+y^3=26\)
b) x + y = a
\(\Rightarrow\left(x+y\right)^2=a^2\)
\(\Rightarrow x^2+y^2+2xy=a^2\)
\(\Rightarrow b+2xy=a^2\)
\(\Rightarrow2xy=a^2-b\)
\(\Rightarrow xy=\dfrac{a^2-b}{2}\)
Do đó:
\(x^3+y^3=\left(x+y\right)\left(x^2+y^2-xy\right)\)
\(\Rightarrow x^3+y^3=a\left[b-\left(\dfrac{a^2-b}{2}\right)\right]\)
