Question

Tính GTBT

a,cho x+y=3 va x²+y²=5

Tính x³+y³

b,cho x-y=5 va x²+y²=15

Tính x^3-y³

^{cac ban giup minh nha}

Answer 1

a)

Ta có :

\(x+y=3\)

\(x^2+y^2=5\Leftrightarrow\left(x+y\right)^2-2xy=5\Leftrightarrow9-2xy=5\Leftrightarrow2xy=4\Rightarrow xy=2\)

\(x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)=3.\left(5-2\right)=9\)

b)

Ta có :

\(x-y=5\)

\(x^2+y^2=15\Leftrightarrow\left(x-y\right)^2+2xy=15\Leftrightarrow25+2xy=15\Rightarrow xy=-5\)

=> \(x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)=\left(5\right)\left(15+-5\right)=50\)