Toan 8 cua vu huu binh

R

ronaldover7

cho $x+y=a$ va $x^2+y^2=b$,Tinh $x^3+y^3$ theo a va b
$x^3+y^3=(x+y)^3-3xy(x+y)=a^3-3axy$
Ta có: $(x+y)^2=x^2+y^2+2xy$ \Rightarrow $a^2=b+2xy$
\Rightarrow $xy=\frac{b-a^2}{2} $
\Rightarrow $x^3+y^3=(x+y)^3-3xy(x+y)=a^3-3axy=a^3-3a\frac{b-a^2}{2} $
 
E

eye_smile

Có: $x^3+y^3=(x+y)(x^2-xy+y^2)=a(b-xy)$

Có: $xy=\dfrac{(x+y)^2-x^2-y^2}{2}=\dfrac{a^2-b}{2}$

\Rightarrow $x^3+y^3=a(b-\dfrac{a^2-b}{2})=....$
 
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